Plain-language case for risk-neutral discounting
Question
Without equations, explain to someone with no maths background why the Black-Scholes model uses the risk-free rate instead of the stock's expected return.
Short answer
Because the option can be copied exactly with stock and borrowing, so its price is pinned by that recipe, not by anyone's forecast. A trader can combine the option with the right amount of stock so that gains on one cancel losses on the other; that combination is riskless, so it can only earn the safe rate. The stock's expected return is already built into today's stock price, so it does not need to appear again.
Adapted from Crack, Heard on the Street, Q2.49, p.31; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- The Black-Scholes PDE, Formula and Implied Volatility
- Expectation, Mean, and Variance
- Conditional Expectation and Variance Revisited
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