Reddit Posts
Is there an advantage to using the BSM versus the Heston model for pricing call warrants?
Please comment on draft Black-Scholes-Merton Excel spreadsheet & graphics application
BSM High Call Volume. Should I follow the trade.
Wall Street Week Ahead for the trading week beginning April 10th, 2023
Wall Street Week Ahead for the trading week beginning April 10th, 2023
Why B$M is a Strong Investment: A Look at its Financial and Historical Performance
Options are sophisticated gambling (for small players). Is it not?
Volatility and You: How Underhedging Creates Crashes
Spire Global ($SPIR) DD – Easy Peasy SPIR Squeezy
Why Retail Traders Should Avoid The Kelly Criterion Method
Math details - in what sense is Black Scholes optimal?
The hidden link between $GME and $PRPL
Mentions
My understanding is that prior to entering any trade, one should figure out the math on the following: 1. Delta - probability that an option expires ITM (this can and does change during the life of the option); available from options chains 2. Probability of Profit 3. Probability of Max Profit 4. Risk / return = (1 - Probability of Max Profit) / Profitability of Max Loss? I think this was the formula I saw on Option Alpha 5. Expected value - avg. outcome of a trade based on the probability of max profit Is this right? How do I calculate 2,3, and 4 for any trade? I've looked in so many places and have seen so many differing formulas with no clear consensus. This author calculates it using d2 in the BSM model: [https://medium.com/@rgaveiga/probability-of-profit-of-an-options-strategy-from-the-black-scholes-model-6146585f0fa0](https://medium.com/@rgaveiga/probability-of-profit-of-an-options-strategy-from-the-black-scholes-model-6146585f0fa0) Others like TastyTrade use calculus. Which matters more PoP or Probability of Max profit considering that most traders don't even hang on to the trades until expiration? Am I also correct to assume that there is a tradeoff between PoP and EV? i.e. Higher PoP has lower EV and vice versa?
Gotta say thank you again. I was using real time stock prices but neglecting to do real time company analysis. I missed the update yesterday that Viking is expanding capacity with Catalent. Updated commentary: # VKTX (Viking Therapeutics) - Executive Summary **1. The Fundamental Check (The "Why" Filter):** VKTX is heavily shorted by institutions betting that the clinical-stage biotech lacks the manufacturing capacity to compete against heavyweights like Eli Lilly and Novo Nordisk in the GLP-1 weight-loss sector. However, executing the Counter-Thesis Search Mandate reveals this bear thesis is critically flawed: VKTX recently finalized a massive manufacturing and supply agreement with CordenPharma to provide large-scale supply and fill/finish capacity for both subcutaneous and oral VK2735 formulations. Management confirmed this provides capacity for a multibillion-dollar revenue opportunity. The shorts are trapped in an obsolete narrative, while bulls are trading on advanced Phase III trials and recent M&A takeover speculation. **2. The Convergence Check (Dual-Model Validation):** * **BSM Prob 1 ($45.00 Upper Channel/Call Wall):** 23.04% * **MC Prob 1 ($45.00 Upper Channel/Call Wall):** 11.56% * **Status:** **DIVERGENT (Trust MC - BSM Over-Optimistic)** * *Commentary:* The BSM model is being artificially inflated by a high 72.9% Implied Volatility. While a spike to the $45.00 resistance is theoretically possible, the Monte Carlo path simulation shows that in over 88% of simulated realities, the stock fails to reach and hold that level before April 17th. **3. The Fat Tail Check (The "Squeeze" Filter):** * **Short Interest:** 23.20% (High Pressure) * **Days to Cover:** 10.86 Days (Extreme Bottleneck) * **Borrow Rate:** 0.37% (No Financial Pain) * *Commentary:* No Fat Tail Flag appended. While the 10.86 Days to Cover creates a severe exit bottleneck, the negligible 0.37% Borrow Rate means the shorts are not bleeding capital. They are not trapped by carrying costs; they are simply waiting out the clock. **4. The Output Format (The Final Synthesis):** "Our dual-model probability engine yields a **23.04%** theoretical (BSM) probability and a **11.56%** pathwise (Monte Carlo) probability of reaching the **$45.00** Ignition Point (a **29.12%** ROI) by the **April 17, 2026** options expiration. For the **$92.72** Exhaustion Ceiling, the models show a **0.00%** (BSM) and **0.00%** (MC) probability. **Synthesis:** Because the models are **DIVERGENT**, the **11.56% MC** probability is the more mathematically sound expectation. The 11.48% gap indicates the BSM model is artificially inflated by sector-wide Implied Volatility, while pathwise simulations reveal the stock lacks the sustained momentum required to breach the upper target. Note: This stock is in the Biotechnology sector, which is currently experiencing high M&A speculation and volatility surrounding GLP-1 pipeline advancements." **The Risk/Reward Verdict:** * **Floor Risk (Tier 3 - Warning):** 12.51% drop to the $30.49 algorithmic support floor. * **Risk/Reward Ratio (Target 1):** 1 : 2.33 * **Verdict:** **HOLD.** With a Divergent Convergence Check and a Tier 3 risk profile, the math does not support deploying capital purely for a short squeeze today. Despite the strong fundamental counter-thesis and the extreme Days to Cover bottleneck, the shorts are not financially pressured to cover immediately, and the pathwise probability (11.56%) of hitting the ignition point is too low to justify a 12.51% downside risk.
Thoughts? # VKTX (Viking Therapeutics) - Executive Summary **1. The Fundamental Check (The "Why" Filter):** VKTX is a high-profile battleground in the GLP-1 weight-loss sector. Institutional shorts are betting against their cash burn and potential inability to compete long-term with the manufacturing scale of Eli Lilly and Novo Nordisk. Bulls are trading on the recent advancement of their oral Phase 3 trials and intense M&A takeover speculation. **2. The Convergence Check (Dual-Model Validation):** * **BSM Prob 1 ($45.00 Upper Channel/Call Wall):** 28.62% * **MC Prob 1 ($45.00 Upper Channel/Call Wall):** 14.44% * **Status:** **DIVERGENT (Trust MC - BSM Over-Optimistic)** * *Commentary:* The BSM model is being heavily skewed by the massive 85% Implied Volatility surrounding the obesity sector. While a spike to the $45.00 resistance is theoretically possible, the Monte Carlo path simulation shows that in over 85% of simulated realities, the stock fails to reach and hold that level before April 17th. **3. The Fat Tail Check (The "Squeeze" Filter):** * **Short Interest:** 23.20% (High Pressure) * **Days to Cover:** 10.86 Days (Extreme Bottleneck) * **Borrow Rate:** 0.37% (No Financial Pain) * *Commentary:* No Fat Tail Flag appended. While the 10.86 Days to Cover creates a severe exit bottleneck, the near-zero Borrow Rate means the shorts are not bleeding capital. They are not trapped; they are simply waiting. **4. The Output Format (The Final Synthesis):** "Our dual-model probability engine yields a **28.62%** theoretical (BSM) probability and a **14.44%** pathwise (Monte Carlo) probability of reaching the **$45.00** Ignition Point (a **29.20%** ROI) by the **April 17, 2026** options expiration. For the **$92.72** Exhaustion Ceiling, the models show a **0.02%** (BSM) and **0.01%** (MC) probability. **Synthesis:** Because the models are **DIVERGENT**, the **14.44% MC** probability is the more mathematically sound expectation. The 14.18% gap indicates the BSM model is artificially inflated by extreme sector Implied Volatility, while pathwise simulations reveal the stock struggles to sustain the required momentum. Note: This stock is in the Biotechnology sector, which is currently experiencing high M&A speculation and volatility surrounding GLP-1 pipeline advancements." **The Risk/Reward Verdict:** * **Floor Risk (Tier 3 - Warning):** 12.46% drop to the $30.49 accumulated volume support floor. * **Risk/Reward Ratio (Target 1):** 1 : 2.34 * **Verdict:** **HOLD.** With a Divergent Convergence Check and a Tier 3 risk profile, the math does not support deploying capital purely for a short squeeze today. The shorts are not financially pressured to cover, and the pathwise probability (14.44%) of hitting the ignition point is too low to justify a 12.46% downside risk.
Thank you for this, by the way. Monte Carlo is a great second model to use so I've updated my process to run both BSM and Monte. This is exactly what I was hoping to get out of this post so even though it was locked, I really appreciate your feedback. Here is an example modification to my output: # Example Case Study: LEU (Centrus Energy) Look at the results from the simulation I just ran for you: * **BSM Probability:** **39.15%** * **Monte Carlo Probability:** **19.74%** * **Convergence Gap:** **19.41%** * **Verdict:** **DIVERGENT.** **Commentary:** "BSM is being tricked by the high 85% Implied Volatility. While the $245 strike looks like a magnet, the Monte Carlo simulation shows that in 80% of realities, the stock fails to reach that level before April 17th. This suggests that the $245 'Ignition Point' is a harder ceiling than it looks on paper.
# PATH (UiPath) - Playbook Analysis **The Narrative (Phase 1):** UiPath is the leader in Robotic Process Automation (RPA), now pivoting hard into "Agentic AI." While they have an incredible 16-quarter streak of beating EPS estimates, the stock has been hammered recently (-37% in 3 months) due to fears that generative AI might make traditional RPA obsolete. Today's earnings call is their chance to prove their new AI agents can drive actual revenue. **The Pressure (Phase 3):** * **Short Interest:** **20.16%** of the float. * **Days to Cover:** **2.07 Days**. **(Moderate Pressure)**. * **Borrow Rate:** **0.33%**. **(FAIL - No Financial Pain)**. * *Summary:* Shorts have built a significant position ahead of earnings, but with a 2-day exit window and almost zero cost to hold, they aren't "trapped" yet. They are positioned for a miss. **The Magnet (Phase 4):** The primary Gamma Call Wall is sitting at the **$14.00** strike for the April expiration, which aligns with several recent analyst downgrades that set $14-15 as the "new" fair value. **The Math (Phase 10):** *"Our customized Black-Scholes-Merton model indicates a* ***48.85%*** *probability of reaching the* ***$14.00*** *Ignition Point (a* ***17.85%*** *ROI), and an* ***8.27%*** *probability of reaching the* ***$19.00*** *Exhaustion Ceiling (a* ***59.93%*** *ROI) by the* ***April 17, 2026*** *options expiration."* **The Reward Distribution (Phase 7):** * **Target 1 - Ignition Point ($14.00):** \* **Risk/Reward Ratio:** **1 : 3.53** (Strong). * **Target 2 - Exhaustion Ceiling ($19.00):** *Metric: High Analyst Target / 52-week Peak.* * **Risk/Reward Ratio:** **1 : 11.87**. **The Risk (Phase 6):** The structural floor is **$11.28** (Key technical support). * **Max Downside:** **5.05%**. * **Risk Tier:** **Tier 2 (Standard)**. **Verdict:** **EARNINGS SPECULATION.** Standard BSM math doesn't "know" earnings are tonight, but it *does* see the massive **92% Implied Volatility**. You are risking a 5% drop to the support floor for a near-coin-flip (48.8%) chance at a 17.8% gain. If they beat and raise guidance, the 20% short interest will have to scramble to cover into that 2-day bottleneck, likely blowing past $14.
Agree about BSM especially in this current market. Anyway, here you go: # BNO (United States Brent Oil Fund) - Playbook Analysis **The Narrative (Phase 1):** BNO tracks Brent Crude oil futures. As of March 2026, it is the center of a massive geopolitical tug-of-war. Prices have surged to 52-week highs following supply disruption fears in the Strait of Hormuz. You aren't trading a stock here; you are trading global instability and the risk of an Iranian blockade. **The Pressure (Phase 3):** * **Short Interest:** Negligible (typical for commodity ETFs, as traders use futures for shorting). * **Borrow Rate:** **\~1.00%**. **(FAIL - No Squeeze Pressure)**. * *Summary:* This is a pure momentum play, not a short squeeze. There is no "trapped" shorts mechanic here because commodity ETPs have an elastic share creation/redemption process. **The Magnet (Phase 4):** Heavy call concentration is currently sitting at the **$48.00** strike for April 17th. **The Math (Phase 10):** *"Our customized Black-Scholes-Merton model indicates a* ***56.68%*** *probability of reaching the* ***$48.00*** *Ignition Point (a* ***9.49%*** *ROI), and a* ***25.60%*** *probability of reaching the* ***$53.09*** *Exhaustion Ceiling (a* ***21.10%*** *ROI) by the* ***April 17, 2026*** *options expiration."* **The Reward Distribution (Phase 7):** * **Target 1 - Ignition Point ($48.00):** \* **Risk/Reward Ratio:** **1 : 0.80** (Weak). * **Target 2 - Exhaustion Ceiling ($53.09):** *Metric: Momentum Projected High.* * **Risk/Reward Ratio:** **1 : 1.79**. **The Risk (Phase 6):** The structural floor (today's session low) is **$38.66**. * **Max Downside:** **11.82%**. * **Risk Tier:** **Tier 3 (Warning)**. **Verdict:** **AVOID (For Squeezes).** This is a momentum trade, not a squeeze. The math actually shows a poor risk/reward ratio because the downside floor is so far away (11.8%) compared to the immediate upside.
Thanks! Here's my thinking.... Jars? Who makes jars. MASON. Mason? What does a mason use. STONE. Stone? BlackStoneMaterials. $BSM. Looks good. Im in! About as good of DD as you will find anywhere else
Thanks for clarifying. Well, we assume that the current underlying level is roughly the most likely outcome in the future* And because we use dollars (or other currency) to represent these probabilities (as cash premium), it follows that the ATM options roughly have the highest volatility premium** And because computing vega contemplates option price (given a hypothetical change in volatility), vega will be high ATM (where the vol price is highest)*** ... But what about vomma? We want to know how much our vega changes when volatility increases. Well, when volatility increases, a broader range of outcomes is considered more probable. Ie, the less probable outcomes (eg, OTM options becoming ITM) are now relatively more probable (more premium). Vega contemplates option premium, so with higher volatility, OTM options have a higher vega. A "moderately OTM" option vega will get a bigger boost than either the ATM or deep OTM option vega. For this part, my best "intuitive" reasoning (instead of looking at the second derivative of a pricing model's cdf) is that these strikes have the particular convex behavior because they are an optimal balance of notional leverage (eg, relatively low cash premium, also mathematically creating a smaller denominator for price changes like for vol shocks) but still having enough absolute premium to have a meaningfully large cash premium increase when the shock happens. Anyway, all this is ultimately based on expectations of asset price behaviors (which the models are supposed to capture). Vega (and therefore vomma) calculations are only useful if you believe the models and their assumptions are reasonable. However, plenty of market phenomena exist with or without a name or formula (like volatility convexity). *Based on the pdf function used in models like BSM. Might exclude some factors like drift **Option price (including the vol premium) is commonly modeled as a function of strike relative to current underlying price as an input into a cdf/pdf function (probability). So strike --> probability --> price. ***vega is the partial derivative with respect to volatility of option price components
Vega vs vol As vol increases: 1. vega increases for the wings 2. [vega] remains constant for the atm 3. [vega] increases more for call and less for put 4. This is according to BSM pricing model Are these your claims? As a sanity check: are you familiar with "vomma"? (I'm trying to understand if you literally mean increases in vega and not increases in option price due to vega) Just trying to prevent confusion in the conversation
Yes, this thread really helps me spell it out. You're a part of that, thanks! I really botched the original post, so much so people thought I am claiming there's no probability in BSM equations, or that I am a denialist of the model. There is, but it's not about odds of a trade, or what will happen in the future. The original post also lacks "so what", which makes it twice as aggravatingly incomplete. :D I believe that learning about options is confusing, and the bar is set high. Even for someone coming with experience in stock picking and technical analysis. Most people won't start with Natenberg, or will immediately pivot to easier explainers. That's when they get equipped with mental crutches to get started, but "pick 0.60-0.70 Delta" advice is a poor substitute for risk management.
Models are great when they are used for the right task. Greeks and IV help you determine whether it's worth it in pricing and reward terms. We need common language for options markets to function reliably. BSM provides just that. Then unknown variables matter for decision making about a trade as a whole. If I were to use tools that ignore existence of external variables, I end up using a mental crutch. Using BSM and Delta for decision making means relying on tools that are deliberately underfit for the real world. The thing that applies broadly to my trading (longer-dated directional) is that markets price in expectations about the future, not the future. Future can't be observed, facts can, and expectations will shift when there are new facts.
The BSM partial differential equation doesn’t have N(d1). Coming from a statistical perspective, sure N(d1) is an output and an input. Nevertheless delta is easy to calculate, you’d never use a pricing model to figure it out.
Absolutely, that's why Market Makers and sell-side traders collect variance risk premium. I'd say Delta is one of the outputs, but the broader bias comes structurally from how the entire model works. The premium is forward-looking in origin (by BSM standards), it exists because of what markets fear might happen. Realized volatility is very often lower, which gives sellers a structural advantage. Now, sellers primarily draw advantage from IV and Theta Decay. They can hedge against Delta, and the real danger is Gamma. Also, notice how in Covered Calls traders need to already be fully hedged. People going long are at a disadvantage because of that, and this is why they need to be forward-looking of what may happen before market even prices it in. Buyers need an edge that comes from outside the model, because the model's assumptions create a limited, backward-looking view of what the market may actually do. It is also a matter of when. When you are buying Delta in high IV environment, you are exposing yourself to the risk that realized volatility will likely be lower on top of paying high premium. Then if you are buying it in low IV environment, you are getting bargain prices, but you bet that market will deliver new inputs to the model that will shake up pricing of options, underlying, and Delta. Now, no risk manager working for MMs or sell-side trader will try to guess catalysts and moves, because they are managing short-term risk per model output based on current conditions. Buyers should be looking for opportunities that will shock the inputs – and this is outside the scope of Delta.
Nothing about BSM has predictive value, so that's not the gotcha you think it is.
Look, we all know that BSM is a model, and that it has assumptions about the world. I'm actually happy it does. Yet somehow Delta ends up pulled outside that mathematical model as a proxy of ITM probability. It then gets used to drive trading decisions, which fall way outside of what BSM describes. **Therefore traders misappropriate Delta in 2 ways:** 1. Outright category error. Delta is a construct internal to BSM, never designed to describe real-world probability. 2. Tool misappropriation. Delta is a hedging tool for MMs maintaining delta-neutrality, not a directional target for traders taking positions. Yes, Market Makers act on gamma exposure, and hedging affects price action. Now, **what Delta really tells traders** – only when combined with strikes and OI – is how aggressively MMs will hedge along the path towards every expiration. It matters the most to people trading contracts nearing their expiration.
Yes, point 2. N(d_2) is risk-neutral probability. It's a mathematical construct(?) for safeguarding against price arbitrage (by BSM's assumptions). N(d_2) ensures the model is internally consistent. Nowhere near any predictive value.
No, delta is universally taught that it can be used as a rough measure of probability, not that it is probability. The actual probability is N(d_2), delta is N(d_1) in the BSM.
The feeling I get is that the wheel is used by folks who are looking for a modest, regular generation of cash for current consumption (paying electric bill, car bill, taking spouse out to dinner) while preserving capital. It's a poor choice, in my opinion, if you are interested in growth. Strong proponents of the wheel will tell you that a big drawdown shouldn't happen ("you picked the wrong stock") or that you should be happy to hold it for months while it recovers. A bit out of touch if you ask me. The strategy is three pronged: buy high (via a cash secured put), sell low (via a covered call) and hope to make up the difference in premiums received. You may think to yourself, "why not limit my downside risk with the short (cash secured) put by doing a vertical?". Smart move, but don't go over to the ~~locked, deleted and removed posts~~ wheel subreddit as you're likely to be met by harsh words, have your post locked and perhaps removed, and if done repeatedly, banned. Don't let that bother you. Good risk management practice outweighs what one loud individual says. If you decide to enter via a short put, verticals can be a good idea. I prefer doing buy/writes. While you're out there selling 30 delta puts waiting to get assigned, I just buy the stock and sell an ATM call. Of course, if I was interested in growth, I could sell it a bit OTM, but my long-term positions have that covered. (My long-term positions are for growth, buy/writes are for current cash generation. If interested, check my profile for my sub where I've lately been posting my short call activity). To be honest, I'm not sure I've seen anyone who posts their weekly wheel spreadsheets beating SPY much less buy and hold. It works best in either choppy markets or, more specifically, with stocks that trade in a narrow range (i.e., low volatility), but then that also means lowered premiums (and lowered possibility of good sized capital gains) compared with a bit more volatility. As u/Connect_Boss6316 says, it's primarily a strategy for a newbie -- as traders gain knowledge and experience they are likely to move on to more advanced options concepts. A trader will want to start trading options, and they buy some calls...poorly. After some losses, they find out about covered calls where the unspoken half-truth is that you can't lose money on a CC as long as your strike is set at/above your 'net stock cost'. Then they learn about cash secured puts. Then they put them together in an options sandwich and find out about the wheel. Some people never advance beyond the wheel for a variety of reasons: poor understanding of options in general, poor understanding of BSM, poor understanding of math/probabilities, poor premium/risk management, etc., and they have no desire to learn and expand their horizons. But I suspect most move on to more rewarding trades.
FWIW, I've been trading options for a living for quite a number of years now, and here's my take: 1) You do need to understand the basics (delta, theta, gamma, vega). You \*don't\* need to become a quant. They're as important and useful as a multi-bit screwdriver - but the screwdriver is just a tool, and doesn't make you money on its own. 2) Understanding market mechanics, the auction process, where the price-insensitive traders hang out, and when they \_must\_ trade is HUGELY more important than the ability to re-derive the BSM. 3) As a pocket friend of mine put it, play defensive games against drunk rich guys who just want to have fun. I just published a book about how I got to where I am - mistakes included - and it's all about how to become a trader by \*using\* the tools instead of hyperfocusing on them. If you're interested, it's on Amazon; "Navigating Stocks and Options: The Captain’s Log". In any case, good luck with your trading!
There is no broker price to trade at - their calculations are theoretical, for information only. So there is market price, broker theoretical price, and my own fair value price. Since brokers and most of the market use some variation of BSM, the market prices are close to whatever the broker calculates as theoretical price. None of this matters. I compare my own price to the market price, and make my trading decisions.
Thanks for sharing! I'm curious, when you go to place the order with your broker, aren't they all using the BSM model anyway? Wouldn't you have to accept whatever the broker pricing is telling you if you want to get a fill? Or do you just wait until the price of the setup falls to your 'fair' pricing setup?
Yes, good thinking for a practicioner, BSM assumptions make the model too theoretical Im researching a binomial model to estimate up and downtrends to provide a more realistic pricing
Of course I do and I have created the "rank" to signify the deviation aawy from BSM. The higher the rank the greater the deviation. Rank is rounded numbers 1 to 5 on purpose to prevent reverse engineering.
This all makes sense. I think yes, management of open positions would interest me the most. But I suspect my use case isn't so different from other users' when we reframe the pieces. Let's generalize: * Future market possibility (eg, stock moves up, etc) * Potential action (eg, buy, sell, hold some position) * Expected result (eg, gain/lose X amount over 20 days, etc) We can mix and match these. "Future market possibility" (scenario) could be a speculative belief (eg, stock moves -5% on earnings in 12 days) or a hedge scenario (what if us crude oil moves against me by 10% by the end of 3 months?). Now you can serve speculation and hedging user needs. Someone may want multiple variants of a single scenario (eg, up 5% vs up 7%, stock up + vol up vs stock up + vol down, etc, etc, etc). "Potential action" can be customer defined ("I'm already interested in buying SPY puts" maybe I just don't know which expiration, etc) or recommended ("these 25 ETF puts have the highest IV-to-HV ratio..."). Sounds like you already do the recommendations, but I didn't quite understand how that's presented. And again, there could be variations (eg strike A1 vs A2, sell within 15 days vs sell at expiration, etc) including "make no portfolio changes." "Expected result" could be simple (eg, value at a future point in time assuming all contracts carried to expiration, etc) or more interpretive (eg, using BSM vs BS pricing models). It could also be bracketed/Monte Carlo'd (eg, EV if early assignment and no downside move beyond strike A1, etc). Sounds like you're currently focusing on value of a hypothetical position at expiration.(Ie, we could extend to imagine one "potential action" having a bunch of "expected results", if only due to different future points in time). So what I'm saying is by generalizing the pieces needed to take someone from possibility to action, you can serve lots of different customer use cases with the same framework. Also the framework lets you plug in new features (eg, new pricing models which have different potential revenue and costs to operate). Maybe you're already doing this. Also... You could even perform all of this recursively (possibly even in a chat bot). Eg, "assuming the S&P500 will not drop 5% in the next 45 days [speculation scenario], what SPY put could I sell to maximize ROC with a drawdown of no more than 40%?" Might return.15 different sorted contracts to sell [each, a potential action]. And then you ask, "assuming SPY rises more than 1% in the next 24 hours [hedge scenario] what are the times and prices to submit sell limit orders [potential action] for 3x the March 580P to maximize the premium collected but not going more than 8 hours at a time without increasing position risk?" [Expected result]. We used the framework to identify a 45 DTE position and again to hedge against getting a bad entry on that recommendation. Does this seem possible and valuable to you? So my more concrete feedback on the tool is that it wasn't obvious how I would use it for my use case (mostly hedging). But by generalizing the features, it could be much easier to draw in many types of users and use cases because it will be more seamless to "brand" each feature for different use cases (eg, you could have a "hedge builder" and "speculation lab" both run on the same framework but be easier for users to understand what it can do for them) I know these can be very big projects, so the idea here isn't to flood you with "do my use case!" Or "I don't get it" but rather to think out loud about how we can simplify solving these kinds of problems, partly as way of assessing a tool's current value as well as total addressable user needs.
Remember BSM, if it's not IV or price, then it surely is the risk-free rate, so go check bonds. In all seriousness, obviously IV has shot up during the weekend. Like do you seriously think that the market has not adjusted it's view on volatility after what happened on Saturday because the equities are closed and the data is not being disseminated?
This is the original trading method used by Scholes and Morton. Yes the two guys that came up with BSM model. It does make money, but it is not easy. Evidently by their fund blew up in 1998.
You think people here have the attention span to learn about the possible option structures they could use or things like the BSM model and option pricing? Hahahahahaha
I like BSM and have \~3,800 shares. I am a long term holder looking to add more. The long term thesis looks strong for natural gas prices and volume, with growing electricity demand and gas likely to be a source of supply for the next few years while nukes and solar+battery tech gets added to the grid. Nevertheless, I am going to wait a bit longer. I used to try to pick the bottoms but have had better results waiting for a reversal and then buying.
Most listed equity options are American exercise, so strictly speaking, closed form BSM doesn't apply. Practically, it's still a good approach to try it out to see how it works in it's simplest form. You should find lots of existing answers to these simply questions in places like Quant stack exchange or any decent textbook about derivatives pricing. For your questions specifically, while closed form theta (per day) can exceed the option price, it's per unit time and you need to convert the annual value to daily values, see https://quant.stackexchange.com/a/82181/54838. I disagree with using 250 or so trading days because every professional tool used at least minutes to expiry for full days. That's why the VIX itself is also computed using calendar days and the white paper states that **it divides each day into minutes in order to replicate the precision that is commonly used by professional option and volatility traders**. Hence, the VIX formula uses 525600 in the denominator. Vega also needs to be scaled by *0.01. That's why it's always good practice to also compute finite difference Greeks: - Vega: https://quant.stackexchange.com/a/69775/54838 - Theta: https://quant.stackexchange.com/a/82181/54838
I don’t really think ENVX and BSM similar
>Challenge was funds I often say the most expensive options are the cheap ones. ;-) BSM: [https://goodcalculators.com/black-scholes-calculator/](https://goodcalculators.com/black-scholes-calculator/)
Thanks for explaining with example. Challenge was funds, but I see your point that 80 delta is less risky as high chance of becoming profitable. Mind sharing which BSM calculator did you use please?
u/TheInkDon1 and I are on the same page. You're fortunate he responded before I did, as while my core message would be the same, my response to your question "I am wondering how long should I wait before closing it?" would have been "One minute after you bought it." 😉 > if I had bought ITM, wouldn't I lose more money when price goes down as was the case here i.e from 252->233? Let's take a look. You bought the Jan 16, 2026 $250 call on Oct 21 (88 DTE) for $6.30. IV \~46. On Oct 21, AMZN closed at $222. Using a BSM calculator, I see a $190 on that day yielding a 80 delta. It's price was \~$36.88. That Jan 16, 2026 $190 call is now worth $45.30, a gain of $8.42/share. A 23% gain. Instead of a 34% loss, you'd have a 23% gain. You're making a mental mistake by looking at "252-233": what does that matter? What matters is you hold an asset that has declined by 34%; if you had bought an 80 delta, you'd be up 23%.
guy above already answered, to elaborate options have always existed and traded, they have an exchange with CBOE, the modern options pricing theory started Bachelier Model in the early 1900s, which then matured under BSM model devised by Black, Scholes, and Merton (as the name BSM suggest)
yeah this isn't really accurate. BSM is used to derive elements of the pricing model but the crux is how vol is forecasted. that's what determines everything. so you're not really solving for the right thing here. the implied vol we pull from options chains includes probability of jumps, diffusion, shocks, skews, kurtosis, event risk, etc. small caveat for clarity, thinkorswim for example uses Bjerksund-Stensland for greeks, not BSM because of early exercise inclusion.
Perhaps this disparity in Burry’s perception vs market reality is that the golden era of inefficiency based statistical arbs and latent information is over. It seems like we really don’t have any “cowboys” left in the industry at large the way we used to. Whether we call that a strong form market and attribute it to the flattening of informational edge resultant from computation, or say people are “vibe trading” basis lazy geopolitical info is irrelevant I feel. It’s likely Myron Scholes knew what he was talking about when he used geometric brownian motion as the foundation for the BSM - asset value, outside of pure introduction of liquidity into the markets as we see today, is really a random walk. I guess he’s overfitting his assumptions? I don’t have the experience to really provide an answer, but it seems like he was trying to wrangle the market as opposed to ride the rising avg tide.
For real... it's not like we live in a day age where you can just get on your computer and pull up information on the Treasury (current TGA balance, auction schedules and results, and, quarterly refunding statements), the Fed (RRP and other balance sheet components, etc), and option pricing (the BSM model and it's driving, core mathematical components). You'd need like some super duper Bloomberg terminal for that... or something
Just for fun, plug in the following to a Black-Scholes calculator: * Underlying price: $100 * Strike Price: $10 * Time to expiration: 1 year * Dividend rate: 5% * Risk-free rate: 3% * Volatility: 20% You may notice that the BSM price is less than the intrinsic value. No one would ever sell an American option for less than intrinsic because the buyer could immediately execute it. That means the ask must be at least the intrinsic value and the bid would approximate the fair value.
I should note that taking the limit as something approaches infinity isn't exactly useful in this context but... Under BSM: All of the puts would have a value equal to their strike price discounted by the rfr. And all of the calls would have a value equal to the current underlying price. This is fairly easy to prove by taking the limit of a call or put's price as volatility goes to 100. d1 is equal to s \* sqrt(t) / 2 (which is infinity). Where s is the volatility over the option's period and t is the time to expiration. d2 is equal to -s \* sqrt(t) / 2 (which is negative infinity). So: C = N(inf)S - N(-inf)Ke\^(-rt) = S and P = -N(-inf)S + N(inf)Ke\^(-rt) = Ke\^(-rt) Note: The math above is imprecise (but accurate) to keep my response short.
It might be a harder question than it appears, but it is a good exercise on thinking about calendars. The only definitive payoff line is at expiration; for early time points you need a model. If you choose to use BS, you'll need to either handle non-local volatility or ignore volatility smile. You can alternatively use jump diffusion (Merton) or stochastic volatility (Bates, Heston) instead of non-local IV. I know IBKR uses non-local volatility by fitting the IV curve to a surface, then use that non-local IV on their models for their pricing lines. So there's isn't a simple answer to whether there's a function to do that. Yes, there's a function and libraries (or just calculate BSM yourself), it's just that those results might not be meaningful. That said, payoff lines for calendar spreads aren't always that helpful because they are so vega dependent. If IV doesn't change, simple models' lines might be ok, but the whole point of a calendar is to take advantage of IV changes over time independent of changes to the underlying. You probably need a payoff surface instead of a line (payoff as a function of underlying and IV).
> I’m trading Iron Ore (IODEX) european options on the SGX I'm not familiar with that market, so there might be differences between that market and what I am familiar with, which is US standard exchange-traded options. What follows may not apply to your market. > when trying to reconcile my theoretical prices (using black) with broker quotes. Uh ... that is never a useful thing to do. Instead, you should use BSM to back out IV from the "broker quotes". There is no expectation that BSM, with some random assumption for volatility, should match the market price. You'd have to get insanely lucky to guess a vol that just happens to match a market price. > I’ve noticed that to make my prices line up, I need to manually tweak the Days to Expiry (DTE) — basically adjusting how I count time for theta This is further evidence that your assumption for vol does not correspond to the market price. It's your vol assumption you are supposed to tweak, not DTE. > So my questions Seem to have an underlying assumption that the "broker quotes" are driven entirely by BSM. That would not be the case in the US. In the US, some modeling would be done by *market makers*, and then in most cases, some adjustment to modeled price ranges would be done to build in a profit margin to quotes. Unless the market is very active, like ATM front month SPY calls, the stub orders that establish the bid/ask spread quotes for a low-volume contract would be **discounted** from the modeled price range. This is why it is often possible to fill for a price that is between the bid and ask.
I'm not sure if my post was clear. I never said Monte Carlo was in itself a pricing model, just that it can be used for pricing just like your said. I also said there are closed form solutions to BSM for American options and gave a link to the same citations you gave (a different Wikipedia page that cites the same sources) Everything you said is true, I agree with it, and seems compatible with what I wrote, just with much more (and better) exposition.
Understand how options are actually priced. Learn the BSM model, know how Delta and Vega move with price and volatility, and how all the Greeks interact. Once you understand what truly drives premium, not just direction, you’ll stop guessing and start managing risk. Options are all about risk.
For most liquid underlyings and near-ATM options, Black-Scholes will usually price within a few cents of more complex models. That said, those small price differences aren’t meaningless. They come from how each model treats the volatility surface and distribution tails, and those differences compound when you’re managing multiple strikes, maturities, or a hedged book. Even a few basis-points of mis-pricing per leg can add up in delta-hedged or vol-arb portfolios. Where it really shows, though, is in the shape of the risk landscape. Black-Scholes assumes symmetry: Vega and Gamma peak exactly at ATM, Theta decays evenly. Stochastic-vol or local-vol models reshape that geometry; volatility skew, smile curvature, and term-structure all emerge naturally. So the goal isn’t just to “beat” BSM on one theoretical price, but to see how different dynamics bend both prices *and* Greeks across moneyness and time. That insight is what matters when sizing or hedging real risk.
BSM has always been good enough for me. All the modeling I've done was so close to real prices that it's not worth it to use anything else. Only times where it doesn't work that well is low supply/demand on bad equity, but you'll never get fair price for those.
> skew in the near months(nov-jan) appears to be priced off of a log-normal distribution model(BS). Do you have this backwards? It looks like the higher-DTE options have a flatter IV curve which would imply their forward distribution is closer to log-normal. >Out to 27-28 there is substantial discounting in tmv calls. assuming caused by volatility drag(Heston model). What led you to the idea that tmv calls are discounted? Also, volatility drag can exist outside of the Heston model. In the case of LETFs, I'd argue that the volatility drag reduces the drift rate of the underlying. >Gamma on levered inverse etf options is higher than their levered(non inverse)counterparts when you translate the option’s delta back into the original units. I'd have to think about this more to give a better answer, but my intuition is that this is a model problem. It shouldn't be possible to get cheaper gamma. My guess is that the gamma isn't cheaper, but it appears that way. In order to increase the "price" of gamma exposure, the price of the options goes up, which causes the BSM gamma to go up too. However, this is only meaningful if the option's prices behave how the BSM model 'expects' them to, which you already know isn't true based on your first question about there being skew on some chains. I'm familiar with LETFs, and familiar with options, but tbh, I'm not too familiar with how the two interact. The fact that LETFs have volatility drift that depends on the LETF's target index's return distribution can cause very strange behavior that's difficult to model in the context of options. I'll maybe look into this topic more over the weekend.
Greeks are not linear, so multiplying delta by the change in the underlying's price is only an estimate of how much the option should change. Same thing with theta: Theta itself increases as time to expiration increases. Lastly, Black-Scholes (the equation that is used to calculate Delta, Theta, etc.) is a model of option prices that makes assumptions that aren't true. Options aren't bound to behave consistently with the BSM Greeks.
Yea, 5 delta and lower are hard to price. They don't work well in the BSM model due to these black swan events. Selling them is dangerous for this reason. Buying them can be a cheap hedge, but generally won't pay off unless something crazy happens, like 2008 GCF or covid or other massive events. They almost never pay,but when they do, boy howdy do they print.
IV is a free parameter in the BSM, in other words it's just a number derived from market price, one way you can interpret this number is as the predicted volatility, but it also includes so many other factors i. E skew, vanna, risk reversal , etc that it's really not just as simple as "predicted volatility". IV does not cause volatility, IV is a derived number from supply/demand agreed prices.
"looking at the daily change in options": which daily change are you looking at? If you are looking at "last trade," it could have been a matched ask compared to bid. Options can have a large bid-ask spread. Also they are traded infrequently. One could have happened at opening and the other at closing. The general answer to your question about why an option between two can appear to move less than the others is "don't look at last trade price as an indication of anything because trades happen infrequently and there can be a very large bid-ask spread." Current bid-ask midpoint is probably better. Or roll your own pricing model (e.g., fit the volatility smile then invert it). As for "how are options priced in practice?" Market makers run statistical models (more advanced that BSM) given a set of parameter probability distributions. That gives them probability distributions of outcomes and sensitivity to changes (i.e. the "greeks"). They then pick bids and asks that balance their overall risk while also hedging with the underlying. As prices of underlying and market demand for specific options change, their parameters change and the models are updated, giving new prices. While that's happening, other traders are placing bids and asks inside of the spread. So it's not a simple answer, and confounded by random trades within the spread.
Thanks for pointing out the Deep OTM label.. the optionality of exercise in american options is not being accounted for in this mini study, but why would the optionality of exercise do anything more than guarantee liquidity? I’ve always seen that as a liquidity clause the forces the price to be at minimum intrinsic. My hypothesis for the discrepancy is from the lognormal tails implied by BSM, but your interpretation is interesting. Could you explain more!
Of Course BSM is wrong! It assumes a Gaussian distribuiton of price moves, whereas in the real world, the distribution is much more kurtotic and fat-tailed. Have you tried a Cauchy distribution? It's a much better fit. Or just construct the actual distribution, and interpolate in it.
i chose GME because its known to not be “well-behaved” which is what i seeked to improve with my implied modeling. SPY is obv more standard. Brier loss is the probability equivalent of mean square error on discrete outcomes 1 and 0. I did this to compare the implied probabilities made by delta vs Priced-In (my model). Log loss is a more standard metric, but its pretty sensitive to being far off, and since being ITM is binary… it gives pretty large losses in this case. Its useful here to demonstrate how BSM can be confidently wrong about implied probability/volatility especially at Deep OTM/ITM.
Delta (sensitivity to underlying) actually becomes implied probability if the model is lognormal or binary (degenerate). The way black scholes merton maps to “real world probabilities” is if you believed the current options market pricings were the “best” possible pricing under uncertainty. Except, BSM additionally assumes the underlying to be lognormal. Let me rephrase… lets say I had a “better” way to compute option greeks (the implied sensitivity of the options premium in relation to certain variables), how would you prove that this new model was superior to BSM? What burden of proof would you require? Sorry if my jargon is confusing.
Your question has more to do with discrete time vs continuous time calculations. Assuming your definitions of IV is the 30d ATM IV (which is the default on every platform), it "appears" to increase because the discrete pricing event (i.e. earnings) becomes closer. In reality, the quants pricing the options have always and will always price in discrete events because they're modeling reality outside of the outdated BSM math.
You seem to regurgitate the most common objections to BSM without getting into the crux of the model - it is a yardstick to measure a certain dimension of options, let's call it market demand, and we all know that the yardstick is wrong, but that it can at least offer a value on the dimension on a relative basis. When trading spreads, you care about relative values, and not much about absolutely correct absolute values. "delta is not the implied probability of being ITM" It is commonly used by practitioners as a proxy. Do you even trade or are you a student of accounting? "In other words, you are using the wrong metric, with an imperfect model which doesn't use real-world probabilities." In other other words, I said what I said above - delta as a commonly used proxy for the probability of the option being ITM by expiration can not be used to properly size bets, let along a series of bets with a constantly changing cross correlation.
Page 389, Chapter 18 of Natenburg is a God Send. It will clarify all the doubts. Roughly: ***{N(d1)\* Forward Price of the Stock continuously compounded}*** gives us the average value of all stock prices above the exercise price. Think of this as Conditional VaR where we compute the avg losses once VaR is breached. Similarly ***{N(d1)\* Forward Price of the Stock continuously compounded}*** gives us the average value of all stock prices at expiry date. We then calculate ***{N(d2)\*X}*** which is the average amount we will pay at expiry if we exercise the option \[N(d2) is the probability of option being in the money and X is the exercise price\] Expected value of a call option at expiry would be = ***{N(d1)\* Forward Price of the Stock continuously compounded}*** \- ***{N(d2)\*X} = {N(d1)\* Se\^rt}*** \- ***{N(d2)\*X}*** Now, we need the value of the option today, hence we discount it from expiry day payoff to today Expected value of a call option **TODAY**= *e\^-rt {N(d1)\* Se\^rt* \- *N(d2)\*X}* ***= S\*N(d1) - X\*e\^-rt\*N(d2)*** This is the BSM formula!
Page 389, Chapter 18 of Natenburg is a God Send. It will clarify all the doubts. Roughly: ***{N(d1)\* Forward Price of the Stock continuously compounded}*** gives us the average value of all stock prices above the exercise price. Think of this as Conditional VaR where we compute the avg losses once VaR is breached. Similarly ***{N(d1)\* Forward Price of the Stock continuously compounded}*** gives us the average value of all stock prices at expiry date. We then calculate ***{N(d2)\*X}*** which is the average amount we will pay at expiry if we exercise the option \[N(d2) is the probability of option being in the money and X is the exercise price\] Expected value of a call option at expiry would be = ***{N(d1)\* Forward Price of the Stock continuously compounded}*** \- ***{N(d2)\*X} = {N(d1)\* Se\^rt}*** \- ***{N(d2)\*X}*** Now, we need the value of the option today, hence we discount it from expiry day payoff to today Expected value of a call option **TODAY**= *e\^-rt {N(d1)\* Se\^rt* \- *N(d2)\*X}* ***= S\*N(d1) - X\*e\^-rt\*N(d2)*** This is the BSM formula!
but as the stock goes back and forth you can trade you delta back and forth. Sell high, buy low. This is called gamma 'scalping'. This is what theta decay is accounting for. (plus dividends, borrow and voting rights, yes, yes... I know... cost of capital... alllll parts of BSM model or binomial)
what do you mean by rates? at 10% youre obviously not talking about the risk free rate baked into BSM - you‘re talking about a target return on capital rate?
I'll try to summarise: 1. Download historic EoD OHLC price data for indices, futures, & volatility indices 2. Built BSM to calculate options prices 3. Overlay the logic for the strategy I'm testing e.g. if vol moves above average buy the spread 4. Run the backtest over the historic period e.g. 10 years 5. Summarise results to calculate equity curve & Sharpe Ratio I also use MonteCarlo Simulation to run scenarios for varying price/vol but that's another discussion.
Implied volatility is derived through options market pricing model such as the BSM. It reflects the market’s view on the underlying’s future price volatility.
Part 1 of 2. > What exactly determines the price of an option? The market. As for all exchange trade assets (stocks, funds, bonds, futures, options). If I don't mention a bullet point, assume that I agree that the point is false. > Then I realized that the BS model is mostly used for simplification and explanation. Market makers use more sophisticated models when a new option is first “released” to the market. That's close, but more wrong than right. Many things in the real world are too complex to understand well enough to make useful predictions, including weather, employment numbers, traffic congestion, and option prices. So instead, for each of those complex real world systems, smart people come up with statistical models that have a statistically significant correlation to the real world phenomena, making them *partially* accurate for making predictions. "Statistically significant" does not mean 100% accurate for all time, however. Market makers use BSM for some cases and other models for other cases. They basically pick the most accurate model for the specific use case, with the best trade-offs. For example, one MM may want computational efficiency more than accuracy, because they make markets for thousands of contracts that need updates every tick, while another MM may want more accuracy than computational efficiency, because they specialize in only 2 or 3 series of contracts. It doesn't have anything to do with first release or a contract that is over a year old. > That’s when I realized that a model works backwards, trying to figure out how relevant each of those factors is. That's over-exaggerated. Only one greek, IV, is back-solved out of the model. There's no need to "figure out" whether a greek is relevant or not. It's relevant to the extent that the rate applies to something the user wants to understand. Like if you are driving a car, is the gas gauge more or less relevant than the speedometer? It depends on what you care about in that moment, right? If you got a full tank of gas, who cares what the gas gauge says? But if the warning light of low fuel is blinking, the gas gauge is the most relevant dial on your dashboard. > The thing I thought was the most difficult actually started to make more sense: IV. IV is affected by supply and demand and is somewhat unpredictable. But time, strike, etc, are already known so I assumed the option price must have some backend algorithm that adjusts its value based on maturity, moneyness, and interest rates. BUT how exactly is that determined? IV is affected by **market price** and market price is affected by supply/demand, as well as other things, like sentiment. IV is the *least* predictable greek, because it is affected by market price, which is the least predictable observable in the whole system. > But time, strike, etc, are already known so I assumed the option price must have some backend algorithm that adjusts its value based on maturity, moneyness, and interest rates. BUT how exactly is that determined? 100% false. The market is the only determinant of price. > Trying to answer those questions proved even more difficult. I tried chatgpt, but it told me that the price depends on the Greeks (back to square one). This only proves how persistent this misconception is. Market price comes **first**, everything else, like greeks, come after. This also proves you shouldn't trust LLMs to explain complicated things where there is a lot of misinformation in the training data. > But it’s the market that defines that price the same goes for all the other factors. **FINALLY!** It took a while, but we finally arrived at the one and only truth. (to be continued)
Use a BSM calculator and vary the IV or other parameters like DTE
No one is answering because people are clueless. They are either giving you wrong answers or are making bad jokes to hide their ignorance. The answer is simple: pick your option and see what your broker says the IV is. Then pick the same strike but the first expiration before the event happens - check that options IV. The delta is going to be the expected IV crush. IF you want to translate that into dollars, remove some time value from the post-event option, a week's worth of premium. Or, use the pre-event IV and plug into BSM to price the post-event option and you will get the price you need. Each option will be different because each option contract is its own market place, and some options might be higher or lower in demand, i.e. price, i.e. IV.
No, I’m saying there’s almost no reason for retail to trade because they likely won’t beat a passive index which means they’ve wasted their time, and when they do manage to, it generally is with far worse risk adjusted returns than a leveraged version of the passive investment. That time spent learning to “trade” would bear far more fruit if applied to their primary career. “If you're primarily trading volatility, sure.” Build a stock price simulator, keep it simple, rates and divs at zero, and run 10,000 paths at 20, 40 and 60% vol and compute the value of an ATM put option at the end of those 3 vol regimes. And compare that to the BSM price and Vega of an ATM option priced at 40%. You’ll quickly see that the return is completely driven by the realized volatility over the life of the option vs the implied. You’ll also see that some of the paths under the 20% vol regime will be profitable even if you paid 40%. That just means you got lucky on a particular path. If you buy or sell options you are making a bet on volatility. You should have some basis to believe your estimate of volatility is better than the market’s before you do so. “Implied Volatility is not my estimate vs yours, it's the volatility implied by the current price of the options. You are probably thinking of future realized volatility, which is the truly valuable metric to be able to estimate. Again, even someone with a couple years of professional options experience would understand this well” So here’s what you don’t understand, the market trades in IV terms not in dollar price terms. IV is a more stable parameter where as dollar price changes with every tick of the stock. Professionals build out their vol surfaces and then compute dollar prices.
prolly you want to learn about selling theta at Tastytrade's YT and options in general. For in general, people always recommend big books by McMillan and Natenberg. There's other books that assume basic college math (probability, mostly, but BSM model is dif eq's sidebar this sub and wiki at /r/thetagang will point you at big books but also smaller books by Euan Sinclair, Passarelli and J. Spina.
Beating the market is not some part time thing to do in your spare time. There’s a whole industry trying to get alpha out there. If you do it half heartedly you should expect it to take decades. Nobody will tell you what makes them money because it erodes their advantage. Anyone that tells you how to make money is lying to you, because if it worked they do that instead of selling you something. If you still want to have a crack read the thick books people avoid (options as a strategic investment, BSM model, etc) take all the tasty trade courses and start with backtesting too. Once you have an idea of how to get an edge dip your toes in. Check my posts for other small help
I wouldn't rely on that idea. For each strike and maturity there is a different implied volatility which can be interpreted as the market’s expectation of future volatility between today and the maturity date in the scenario implied by the strike. For instance, out-of-the money puts are natural hedges against a market dislocation (such as caused by the 9/11 attacks on the World Trade Center) which entail a spike in volatility; the implied volatility of out-of-the money puts is thus higher than in-the-money puts. Some people interpret IV as a forward looking measure of standard deviation, just like the commonly used definition of historical / realized vol which is computed as the sample standard deviation of log return as shown [here](https://quant.stackexchange.com/a/71790/54838). However, one should be cautious when comparing IV to historical vol (HV) - also called realized volatility (RV) - because it is not necessarily useful for at least two reasons: 1 ) Empirically, IV tends to overestimate RV, commonly referred to as Volatility Risk Premium. A simple explanation is that market participants tend to overestimate the likelihood of a significant market crash (or are risk averse / seeking insurance against large decline in their long positions) which results in an increased demand for put options. 2 ) IV is the only free parameter in the Black-Scholes-Merton (BSM) model. Higher IV can be a result of compensation for tail risk. As a result, there is no general IV for an option. Quoting from [Just What You Need To Know About Variance Swaps - JP Morgan Equity Derivatives](https://www.sk3w.co/documents/volatility_trading.pdf)
Boundary conditions. At T=0 (expiration), we explicitly know the payoff function of a portfolio consisting of an option and its underlying as a function of the underlying price. That allows solving the BSM differential equation to get price when T !=0.
Option prices are drived by two major blocks within BSM: intrinsic value and time value. Shorter dated options will always be cheaper (assuming no major changes in volatility) than longer dated ones. One-month dated options will still experience fast theta decay as this decay is not linear past the 30-45 day mark. It turns exponential. Buying options should be done after far more research done, not only having an eye on the expiration. Its all about the volatility environment you are in. I advice you to study and research a bit more about options pricing before entering large orders.
AI definitely gave me a more thorough and well rounded response with practical recommendations to my genetic profile. My endocrinologist who had a wait list in one of the most advanced parts of the country said he wasn’t even sure was VDR BSM was and rattled off something he googled in the moment. With AI you have to know what to ask. I can’t be bothered to explain more to you.
What about the higher floor but lower ceiling BSM?
BSM is for European but used for American all day long. Use an OTM fudge for the smile if you insist.
Use BSM as a wrong sized measuring tool, knowing that you are going to have a wrong measurement in absolute terms, but it will be somewhat correct in relative terms. The common heuristic is to use a multiple like 2X on the delta of each vanilla american option in the chain, and then create your one-touch surface based on that. If you have European vanilla options as the only choice, then your factor must be higher than 2. This post is giving me flashbacks of being a sophomore in college and writing a research paper on exotic options named something like "Survey of Exotic Options and Their Applications", and the professor who was an advisor in the Federal Reserve Bank shook his head in dismay as he read the title. I cringe to this day when I think about that moment, but it was an important life lesson he gave me with a single head shake and a bit of purposeful and exaggerated disgust.
Being able to leg into a covered call position is not the same thing as doing a buy-write. Regarding cash-secured puts - let me expand - when you write a put against cash - at RH - RH hold that cash as collateral. RH considers that cash as uninvested - so you cannot earn interest on it. When you write a put - you are impacted by Rho. That is the interest rate that impacts the premium in BSM pricing model. Option traders that write puts expect to have a way to generate at least the risk-free rate on that cash collateral to compensate for the interest rate drag. Most brokers do not lock up your cash when you write a put contract - afaik - RH is the only broker where you cannot generate the risk-free rate on cash when writing puts.
Correct, even though I don't blindly use the POP as calculated by broker software because they use the BSM variations which use gaussian distributions.
Huh? Nothing here makes sense. It peaked at 29.18 like the rest of the market in December 2024. It has grown pretty consistently over the last 5 years from a low of 10 in 2020. I threw some numbers in a random BSM calculator and came up with 1.951 for the stats on that particular option, it's not *incredibly far* off
I think the gist of your question seems to be: will the option decay at a different theta after close if the underlying moves. The short answer is: yes, afterhours moves in the underlying will affect the value (and therefore their greeks) of options even if they're not trading. The full answer is more complicated: All other inputs held constant, the Greeks are calculated based on the current underlying's price and the price of the option. If the underlying moves, the value of the option might not change according to the gamma and delta based on the BSM model (2nd order approximation). If the underlying increases, it may shift the volatility curve (sticky-delta). In other words, the IV may increase and theta according to the BSM model may increase too. Theta may also increase due to the higher value of the underlying (try plugging in the scenario you described into a BSM + Greeks calculator). For example, at K=100, S=100, V=0.5, T=1, rfr=0.05 theta is -8.10119006. With K=100, S=101, V=0.5, T=1, rfr=0.05 theta is -8.15781263. This is all to say that the change in theta is more dependent on the accuracy of the BSM model, the reason that the underlying moved afterhours, and whether the options chain has sticky-strike rather stick-delta-like behaviour.
Most stocks, indices, ETFs, etc. have some skew in their option-implied probability distribution. You'll see this reflected in the BSM delta when you trade straddles centered around the ATM or ATMf. You can fix this by either moving your put further OTM (in most cases) or by purchasing the underlying, as you mentioned. >but that moves the break evens in a skewed way. Yes, the breakevens will be skewed based on the option-implied forward probability distribution. In most cases, probability distribution of an underlying's future expected price is ***not*** symmetrical in log returns (lognormal) or simple returns (normal).
No because the "IV increase" is an artifact of how the greeks are calculated analytically in BSM, which doesn't take special events into account to correct for it you'd have to find the true expected variance of the stock price, usually by looking at the original differential equation with finite time The above is well known and priced in
Using BSM, i calculated the total trade value at $20M and profit of 520M at vix 50.
Me, but I am buying securities, not the market. For example I bought BSM for > 10% dividend yield this morning. Am I too early? Could it sell off and go to 15% yield? Of course it could. But I don't foresee it's dividend being reduced. So If it does sell off, I will live with my regrets and keep holding and collecting 10% divs for a looooong loooong time.
Your brokerage should provide a value of theta based on the Black-Scholes Model somewhere in the option chain. If not, there are most likely free websites that provide that information. Note that BSM is just a model; it is not 100% accurate. Realized theta decay will never match the output of any model perfectly (especially considering there's never really a scenario where all inputs are held constant while time to expiration ticks down).
The cost to borrow is a little bit trickier to calculate than that. The option you mentioned likely has more leverage than you think. You're paying $490 for probably around $3000 of exposure (I'm guessing without looking at the BSM delta) to the S&P 500. Looking at deeper ITM options will give you a better approximation. You can also calculate the option-implied forward price by finding the synthetic future (long call, short put) that has 0 upfront cost, and then derive the risk-free rate from the option-implied forward price.
Correct. BSM does not use option price as an input, however the price of an option based on demand within the market place is used in reverse to solve for Implied Volatility, which affects extrinsic value, which contributes to how wide or narrow the deltas will be with respect to price
"If i recall correctly Black-Scholes doesn't have option price as an input for calculating delta" You are way ahead of yourself asking about delta when you have no basic understanding about how BSM works.
BS/BSM is an option pricing model for European options and gives a good approximation for American-style options. It takes the risk-free rate, implied volatility, call price, share price, time to expiration, strike price and in case of BSM, the dividend of the stock. Like any mathematical equation, if you have five out of six, you can calculate the other. Not sure how your are connecting this with delta which is the change of the option price for $1 change in the underlying stock.
Theta is the same for calls and puts at the same strike by definition if using BSM model. Slight difference if options allow early exercise but the difference is usually insignificant.
"I'm told to use implied volatility" Who told you? It is silly advice, as you have already discovered. I think you may be confused because BSM in textbooks is structured to provide an option price based on known parameter values including volatility. But in the real world future volatility is unobservable so you cannot use BSM to solve for price. But the real world knows the option price because the market shows it. With price already known from the market, the volatility parameter value in BSM can be deduced, i.e. the value is "implied" by the option price (and the other known parameter values). Therefore, if you are trying to use BSM to calculate an option price you must \*select\* a value for the volatility parameter. Selecting (or guessing) that value properly is the key to options trading, the whole enchilada, the full 9 yards. You don't win the game by finding the best price, you win the game by finding "incorrect" implied volatility. In practice, doing that effectively requires skill and effort. Generally it involves a lot of sophisticated statistical modeling and even that is an imperfect science. If you can't do the complex modelling, you are forced to select a value some other way. Selecting historic vol might be a reasonable but imperfect choice.
I thought BSM is for pricing option relative to the HV. Delta of BSM and market price is IV, isnt it?
I had similar problems and Im not sure I overcame them. Isnt implied volatility just difference of BS model and fair market price? If that is not the case, I have a lot to re-learn. I made BS model calculator and its based on 365d volatility and I used risk-free short collar as risk-free rate. My reasoning is higher volatility = higher implied volatility = wider range on short collar (its always near 4%). Then BS model would give fair price for that stock based on HV. Then market price/BSM=IV Or I fucked up - idk
"fudge factor" I'm glad to see I'm not the only one referring to it in that phrase. IV is the one "unknown" in BSM -- you solve for it.
Because the BSM formula for probability of going ITM, N(d2), and the formula for delta, N(d1), differ by only σ√t. So as long as volatility is low or expiration is near, the two formulas are approximately the same.
Implied volatility, for someone telling someone who studied the BSM model for years to learn the basics maybe you should too