Choosing Option Strikes to Trade Implied Versus Realized Volatility
Summary
The document explores how to choose an option strike or maturity for a trade based on a forecast of realized volatility versus implied volatility. It proposes approximating squared implied volatility at a strike by risk-neutral expected average variance conditional on the terminal asset price reaching that strike. It then suggests comparing that quantity with the corresponding physical-measure conditional variance forecast to identify a potentially attractive strike.
This is presented as an initial hypothesis, not a validated trading rule. The post offers no derivation, empirical test, or direct resolution; the sole answer points readers to a quantitative finance textbook. The proposed comparison may omit important features of option returns, including risk premia, the mapping from variance differences to option prices, path dependence, skew, and hedging costs. The same idea is raised for maturity selection, but the document provides no analysis of that extension or evidence that maximizing the stated difference produces the best risk-adjusted trade.
Key ideas
- The proposed strike-selection method compares physical and risk-neutral conditional forecasts of average variance.
- The implied-volatility approximation conditions expected variance on the terminal asset price.
- A larger forecast difference is suggested as a possible indicator of an attractive strike, but is not established as a trading rule.
- The document gives no empirical validation or analysis of hedging, risk premia, or maturity selection.
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# Which strike is the sweet spot for monetizing implied-realized vol? # Which strike is the sweet spot for monetizing implied-realized vol? I actually have two related questions: - Are there articles discussing my question? I'd be interested in not only empirical studies, but especially (semi-) analytical or closed form solutions or approximations and discussions. I have searched for some time, but haven't been able to find anything that really addresses my question. - Due to my inability to find a research paper on this, I am wondering if the following idea of mine will do as a first stab, please feel free to point out errors: By the most likely path approximation the IV can be written as $$ I^2(K,T) \approx E^\mathbb Q \left[ \left. \frac1T \int_0^T \sigma^2_t dt \right| S_T=K \right] $$ where $\sigma_t$ denotes the stochastic spot vol. Suppose now that one has the following forecast / one can evaluate the following expectation: $$ E^\mathbb P \left[ \left. \frac1T \int_0^T \sigma^2_t dt \right| S_T=K \right]. $$ Is the sweet spot then the strike where $$ E^\mathbb P \left[ \left. \frac1T \int_0^T \sigma^2_t dt \right| S_T=K \right] - E^\mathbb Q \left[ \left. \frac1T \int_0^T \sigma^2_t dt \right| S_T=K \right] $$ is maximized? Would this be a reasonable assumption and departure point? The same idea for sweet spot along time to maturity axis instead of strike axis. (Of course also welcome to drop me a message directly if the topic interests you but you can't discuss it here.) ## Answer by Con Fluentsy (score 1) https://quant.stackexchange.com/a/81511 extract from Wilmott Introduction to Quantitative Finance Paul Wilmott I strongly suggest you buy the book. The book is basic knowledge for quantitative traders, Hull is a text, Wilmott is a practitioners book.
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