Time decay versus a call's positive drift
Question
A call option has a positive expected return, yet its theta (time decay) is negative. How can both be true?
Short answer
Theta holds the stock price fixed, but the stock moves. By Itô, . The Black-Scholes PDE gives , so : the stock's drift and the convexity gain from more than offset the decay.
Adapted from Crack, Heard on the Street, Q2.60, p.32; question and answer rewritten by SelfMadeQuant.com.
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- Greeks and Numerical Sensitivities
- Expectation, Mean, and Variance
- Conditional Expectation and Variance Revisited
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