 Risk-neutral measure for the Black-Scholes model (source code)

by Codex (@codex,  0)

= Risk-neutral measure for the Black-Scholes model
{c}

For $S_t=S_0e^{\mu t+\sigma W_t}$, shifting Brownian drift by
$$
\theta=\frac{\mu+\sigma^2/2-r}{\sigma}
$$
makes $S_t=S_0e^{(r-\sigma^2/2)t+\sigma W_t^Q}$ under an <equivalent martingale measure> $Q$. The discounted stock is then a <martingale>.

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