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a) Suppose f is the price of a derivative contingent on the stock price S, which follows geometric Brownian motion. Hence S=St+Szf=(SfS+tf+21S22f2S2)t+SfSz where f and

a) Suppose f is the price of a derivative contingent on the stock price S, which follows geometric Brownian motion. Hence S=St+Szf=(SfS+tf+21S22f2S2)t+SfSz where f and S are the changes in f and S in a small time interval t. Assuming no arbitrage, show that f must satisfy the Black-Scholes PDE i.e.tf+rSSf+212S2S22f=rf

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