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Black-Scholes model

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For a non-dividend-paying stock, a European call with strike $K$ and remaining maturity $\tau$ has value
$$
C(t,S)=S\Phi(d_+)-Ke^{-r\tau}\Phi(d_-),
\qquad
d_\pm=\frac{\log(S/K)+(r\pm\sigma^2/2)\tau}{\sigma\sqrt\tau}.
$$


Black-Scholes formula

Black-Scholes digital option formula

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 29K / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 29K / iv / Solution

Black-Scholes formula

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Black-Scholes formula

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