Estimating Equity Option Volatility Skew from Return Distributions
Summary
The discussion asks whether historical stock returns can be used to estimate volatility skew across option strikes. It distinguishes estimating at-the-money volatility from determining how implied volatility varies for out-of-the-money puts and calls, and questions what skew says about expected returns. The question itself supplies no return series or pricing evidence, so it does not establish a direct conversion from historical volatility to strike-specific implied volatility.
One proposed workflow is to fit one or more GARCH models to daily returns, simulate prices over the option horizon, estimate the resulting probability density, and price options from that density. Implied volatilities and skew can then be inferred from those prices. This is a model-based approximation: its usefulness depends on the GARCH specification, simulation and density estimation, and the assumption that historical dynamics remain relevant. The replies also point to a note on strike-adjusted spreads, without explaining its method in the text.
Key ideas
- Historical volatility alone does not specify implied volatility across option strikes.
- A proposed approach fits GARCH models to daily returns and simulates prices over the target horizon.
- Options can be priced from the simulated price density, then converted to implied volatilities.
- The resulting skew depends on model choice and the assumption that historical return dynamics persist.
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Full text
# Approximating Volatility Skew From historic returns? # Approximating Volatility Skew From historic returns? I was wondering if someone could help me with something. I've been reading more about equity options, and I'm struggling with skew. Conceptually I understand why it exists, what I'm struggling with is how to put a number to it. At-the-money volatility is a straightforward concept by looking at historical moves, but how would I try to approximate skew form this? Let's say I have a stock with these following returns for some period of time, and let's further stipulate that we expect this pattern of returns to be a reasonable approximation for the future. I just made up a series of stock prices, and calculated an estimate of historic volatility. I believe I did the steps, correctly I took the natural log of the (T1/T0) and found the stnadard deviation of it and annualized it. Now I have an estimate of at the money volatility. But how would I go about pricing an option with more skew based on this data? Is there any resource that anyone could point me to that discusses this? Most books just discuss historical volatility, and don't really get into details about how to model skew based on historic returns. Edit: Now let's say that we are asked to price an 115 Strike option, as well as a 90 strike put, and a 140 strike call. For the 115 call, I feel like you could use 80% volatility as calculated below. But for the 90 and 140 options, I feel like you could have incorporate some skew, and I'm not sure how to go about that. I guess fundamentally I'm trying to understand, what skew implies how the returns a stock is expected to have. Volatility tells us how much the market expects a stock to "move". ## Answer by user34971 (score 2) https://quant.stackexchange.com/a/68573 In addition to Kermittfrog's answer, take a look also at this note by Zou and Derman about the `strike adjusted spread', and in particular Appendix B. ## Answer by Kermittfrog (score 1) https://quant.stackexchange.com/a/68572 Disregarding the arguments made against such an idea in the comments to your question, here is what would come to my mind: - Calibrate one (or multiple) GARCH model(s) to your daily return data. - Generate the return (and hence price) density for your time horizon, say one month forward using the corresponding amount of daily simulations. This step may require some density smoother. - Price options directly off the simulated return (hence price) density. - Estimate the IVOL (and skew) from the prices under step 3. HTH?
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