Question: 90. Consider a derivative that pays off si at time T, where St is the stock price at that time. Assume that the stock price

90. Consider a derivative that pays off si at time T,

90. Consider a derivative that pays off si at time T, where St is the stock price at that time. Assume that the stock price follows geometric Brownian motion. Now assume that the price of the derivative can be written as f(t, s) = h(t)s, where h is an unknown function in one variable. (a) By substituting into the partial differential equation (BSM), derive an ordinary differential equation for h. (b) What is the boundary condition for the differential equation for h? (c) Solve the problem for h and hence find the price of the derivative. 90. Consider a derivative that pays off si at time T, where St is the stock price at that time. Assume that the stock price follows geometric Brownian motion. Now assume that the price of the derivative can be written as f(t, s) = h(t)s, where h is an unknown function in one variable. (a) By substituting into the partial differential equation (BSM), derive an ordinary differential equation for h. (b) What is the boundary condition for the differential equation for h? (c) Solve the problem for h and hence find the price of the derivative

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