Volatility Skew Analysis

Volatility Smile as a Distribution Map - Intuition Behind Skew and Fat Tails 1. Why Options Reveal More Than Spot The spot price of an asset reflects its expected value. Options, however, embed the entire risk-neutral distribution. A call option’s value depends not only on whether it ends in-the-money, but also how far it ends in-the-money. Mathematically: The value of a vertical call spread [K,K+ΔK] approximates the probability the stock ends above strike K. A butterfly spread (difference of adjacent call spreads) gives the local probability density at strike K. q(K) ∝ ∂^2C(K)/∂K^2 where q(K) is the implied risk-neutral PDF and C(K) is the call price. This means the volatility surface is a distribution map. 2. Intuition: Two Stylized Distributions Stock A (symmetric “coin flip” case): 50% chance to double (200), 50% chance to collapse (0). Expected value = 100. Options chain is balanced, near-lognormal. Smile is relatively flat. Stock B (biotech “lottery” case): 90% chance to go to zero, 10% chance to hit 1000. Expected value = 100. Deep OTM calls are highly priced (because of tail payoff). Distribution is positively skewed, with extreme fat right tail. Smile slopes upward on the right side. Both trade at $100, yet their option smiles differ radically. 3. Practical Implications for Trading -Skew encodes crash risk OTM puts are expensive because markets consistently overweight downside tails. Selling puts = short crash insurance. Expect high carry but tail blowups. -Calls as “lottery tickets” In skewed distributions (e.g., biotech, tech growth, crypto), far OTM calls trade rich. Buying calls here is not irrational - it’s priced exposure to rare but convex payoffs. -Why Vega ≠ the Full Story Traders often focus on Vega (sensitivity to vol), but the shape of the smile matters more. Example: A 25-delta put can be “overpriced” vs ATM vol but still reflect structural demand (hedgers, insurers). -Smile ≠ Arbitrage A flat Black–Scholes smile is not “truth.” Skew reflects the reality of fat tails. Attempting to fade skew mechanically is dangerous - you’re betting against structural flows and crash insurance buyers. 4. Trading Tips from Practice -Use smile analysis to choose structures: If the skew is steep, put spreads often offer better risk-adjusted carry than naked short puts. Calendar spreads can isolate whether skew is term-structure driven or event-driven. -Look for misalignments across strikes: Compare implied densities via butterflies. Outliers often point to overpriced insurance or underpriced tail optionality. -Respect path dependence: Gamma exposure around skewed strikes is dangerous. Moves into the skew (e.g., spot falling into heavy put OI) can force market makers to hedge aggressively, amplifying moves. Context matters: In indices, skew is mostly left-tail crash risk. In single names, skew can be both downside protection and upside pricing.

Volatility skew in commodity. The geometry that shows who's scared. In equity, the skew tells a familiar story: fat puts because everyone hedges downside. In commodity, the skew is more interesting. It can flip direction by underlying, by maturity, by event. Reading it well is one of the few real edges left in option markets. The 5 things to understand about skew in commodity. 1. What skew actually is The skew is the difference in implied vol across strikes for the same expiry. A symmetric skew (smile) means OTM puts and OTM calls trade at similar implied vol. An asymmetric skew means one wing trades richer than the other. The shape is a snapshot of where the market expects bigger moves and in which direction. 2. Why commodity skew is different from equity Equity carries a structural put skew because long-only investors hedge downside. Commodity has no structural direction. Sometimes the call wing is fatter (oil during supply disruption), sometimes the put wing (crop with bumper-harvest expectation). The skew tells you the current story, not a persistent feature. 3. The skew during Hormuz (live read) With the strait under active threat, the Brent skew has flipped sharply. Fat calls. 25-delta call vol trading meaningfully above 25-delta put vol. That's the market pricing tail risk on supply disruption, refiners hedging future exposure, producers monetizing the premium. The shape tells you who is paying and who is collecting. 4. How to use skew as a positioning signal Extreme skew tells you what positioning is already crowded. When the call wing is bid heavily, retail and corporates are usually the buyers. Pros sometimes fade extreme skew because the premium overpays for the move already priced in. Other times the skew is correctly pricing tail risk and a contrarian fade gets crushed. 5. The mistake most retail makes Buying ATM options when the skew is screaming a directional view. ATM has lower vol but also lower convexity to the move the skew is telegraphing. If the skew says "tail risk to the call side", the OTM call captures the move at a higher convexity per dollar. Reading the skew is choosing the right strike, not just choosing the direction. Skew is the cheapest analysis you can do that the market actually reads. Most traders look only at the ATM vol number. Reading the wings tells you who is positioned where and what move they are paying to be wrong about. Whatever you trade, look at the skew before you place an option. For anyone running an option book in commodity: do you fade extreme skew, or follow it?

Deep Dive: Volatility Surface Explained 1. What is a Volatility Surface? ➔ The volatility surface shows how implied volatility changes across different strikes and different expirations for the same underlying asset. ➔ Instead of assigning a single volatility to an option, the market reveals a "map" of volatilities depending on the moneyness (strike price relative to spot) and the tenor (time to expiry). ➔ In the Bloomberg screenshot above, every number in the grid reflects how much implied volatility deviates at different strikes (30%, 40%, 60%, etc.) and different maturities (1M, 2M, 6M, etc.). ➔ The vertical dimension is time to expiry while the horizontal dimension is moneyness — both axes contribute to the surface's unique shape. 2. Why is the Surface Shaped That Way? ➔ In theory, the Black-Scholes model assumes constant volatility. However, real markets break this assumption. ➔ Volatility Skew: Options with strike prices far below the spot price (deep out-of-the-money puts) often have higher implied volatilities than those close to the money. This reflects investor fear — markets crash faster than they rally. ➔ Volatility Smile: Sometimes options far out-of-the-money and in-the-money both exhibit higher implied volatilities, creating a "smile" shape. This typically appears in assets like foreign exchange rates where extreme movements are equally feared on both sides. ➔ Term Structure: Short-dated and long-dated options have different volatilities because near-term uncertainty is not equal to long-term expectations. ➔ Practical Example: In the Bloomberg table, notice how short-dated (1W, 1M) expiries have sharper variations across moneyness, while longer tenors (1Y, 2Y) show flatter behaviors. Short-term fear creates sharper local volatility shifts, whereas long-term options smooth out short-term noise. 3. How Practitioners Interpret the Surface ➔ Reading the Skew: A trader looking at the surface immediately recognizes if the market is pricing in downside risks (steep skew) or balanced uncertainty (smile). ➔ Volatility Risk Premium: The surface often embeds the premium investors are willing to pay to insure against rare events — skewed surfaces mean higher premiums for crash protection. ➔ Surface Movement: Dynamic changes in the surface across time (like flattening, steepening, or twisting) signal shifts in market sentiment. Example: During major events like a central bank decision, the short-term expiries' implied volatility can spike while longer-term expiries remain stable, causing a deformation in the surface. ➔ Calibration to Models: Quantitative models such as local volatility models or stochastic volatility models must calibrate carefully to the volatility surface rather than assuming a constant volatility input. #quantitativefinance #volatilitysurface #optionspricing #riskmanagement #impliedvolatility #derivatives

For decades, options were viewed as derivative instruments prices derived from the underlying, offering no predictive information beyond the market's consensus volatility. That view is obsolete. Modern research demonstrates that options prices contain forward-looking information about tail risk, jump probabilities, and even future equity returns. The challenge is extracting that signal from noisy market prices. The most robust predictive framework is the volatility risk premium strategy: sell index options (typically out-of-the-money puts) to harvest the premium that reflects the market's overestimation of tail risk. But the edge has been arbed away through crowding. The new frontier is term structure of skew signals. When near-term skew is steep relative to long-term skew, it predicts near-term downside realization. When the term structure inverts (long-term skew steeper than short-term), it predicts a delayed volatility event. More sophisticated models use machine learning on options chains directly feeding the entire surface of implied volatilities across strikes and maturities into gradient boosting models to predict future realized volatility or equity returns. The features are not just levels but shapes: convexity, curvature, and the relative pricing of out-of-the-money puts versus calls. The firms that master options predictive models are not trading options as derivatives; they are trading options as primary information sources about market expectations. #OptionsTrading #VolatilityRiskPremium #ImpliedSkew #PredictiveModels #MachineLearning #QuantResearch #TailRisk

Let's talk about volatility skew. (I wanted to do this for a long time…) I think the most common measures of skew (on the S&P 500) are probably the Cboe SKEW index or the difference of implied volatilities at 95% and 105% moneyness in vol points. And this is where the problem starts: How do you measure skew? You can use moneyness or delta to determine the specific points on the volatility surface. You can also express skew as the difference of these to points or as a ratio. These simple questions already create 4 different measures of skew. As can be seen from the upper 4 charts, those measures behave differently in relation to ATM vol. Based on the “difference measures” the skew is positively correlated with ATM vol, i.e. higher vol = steeper skew. But with the “ratio measures” the result is reversed, i.e. lower vol = steeper skew. Actually, the delta based ratio measure is almost independent from the level of volatility. Btw, the Cboe Skew index most closely resembles the moneyness ratio variant (upper right). So, what is the “right” measure? The answer probably depends on what you are trying to measure. The most obvious use case is to determine if puts are cheap in relation to calls. In this case you would measure the forward return of a delta hedged long risk reversal (short OTM put + long OTM call) in dependence of the skew at initiation. When setting up the risk reversal you can again choose between same strike distance and same delta. So I did this exercise and calculated the correlation of each skew measure with the 10 days forward returns of each risk reversal variant. The results are summarized in the table below. Generally the difference measures (especially delta based) provide a higher correlation with forward returns. So they are a better choice to determine relative cheapness. I also often see skew being used as an indicator for market sentiment, i.e. low skew indicating some sort of complacency as puts are cheap in relation to calls and vice versa. In this case there is weak evidence that implied skew actually predicts forward realized skew, i.e. expensive puts = negative realized skew. This contradicts the complacency view. I guess this is similar to the interpretation of the level of volatility or the VIX as an indicator of complacency. Here also a low VIX is generally interpreted as a sign of complacency, while in fact during bull markets volatility is lower. So I wouldn’t put too much trust in skew as a sentiment gauge. Overall the topic is really complex but fun to look into. Do you use skew and if yes – which is your preferred measure and how do you use it? #options #volatility #VIX #SPX #investing #skew

📢 New paper out! 📄 With Jules Delemotte and Stefano De Marco, we’ve just released: "Refined Expansions of the Skew–Stickiness Ratio in Stochastic Volatility Models" 🔗 Read here: https://lnkd.in/eMxPn7h9 ⚙️ Building on the celebrated Bergomi–Guyon expansion, we derive second-order volatility-of-volatility expansions for the Skew–Stickiness Ratio — an important indicator of implied volatility dynamics — in a broad class of forward variance models. 📊 Tested on SPX-calibrated parameters across: - 📈 Two-factor Bergomi - 📈 Rough Bergomi - 📈 Heston - 📈 Rough Heston 💡 The results show accuracy and provide new analytical tools for understanding smile dynamics. 💻 Code for previous articles: https://lnkd.in/eJweHgyW — new code coming soon! 💬 As always, comments and feedback welcome!