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Risk-neutral measure for the Black-Scholes model

For

S_{t} = S_{0} e^{μ t + σ W_{t}}

, shifting Brownian drift by

θ = \frac{μ + σ ^{2} /2 - r}{σ}

makes

S_{t} = S_{0} e^{(r - σ^{2} /2) t + σ W_{t}^{Q}}

under an equivalent measure

Q

. The discounted stock is then a martingale.

Table of contents 72 2
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