Does mean reversion in the stock change option prices
Question
Compare the price of an option on a traded stock whose price mean-reverts with the price of an option on a stock that does not, other things equal. Does mean reversion matter?
Short answer
Not directly, provided the instantaneous volatility is the same. Mean reversion is a feature of the real-world drift, and replication replaces that drift with the risk-free rate, so it drops out of the price. It matters only indirectly: mean reversion lowers variance over long horizons, so if volatility is estimated from long-horizon returns it will look smaller, and the option will look cheaper.
Adapted from Crack, Heard on the Street, Q2.41, p.30; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Mean-Reverting Diffusions: OU, Vasicek, CIR, and the Feller Condition
- Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
- Option Trading Strategies: Spreads, Combinations, and Payoff Engineering
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