Why mean reversion does not change option prices
Question
A stock's price tends to revert to a long-run level. Why does this not affect the Black-Scholes price of options on it?
Short answer
Mean reversion lives in the drift, and the drift drops out of pricing. Under the risk-neutral measure the stock's drift is replaced by whatever its real-world form; delta hedging removes the directional exposure. Only volatility matters, so mean reversion is relevant only insofar as it changes the volatility you should use (for example, if it reduces variance at longer horizons for a model that is not GBM).
Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.27, p.18; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Market Model and Risk-Neutral Valuation
- Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
- Option Trading Strategies: Spreads, Combinations, and Payoff Engineering
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