What is the boundary condition for the differential equation

Reference no: EM131237515

Consider a derivative that pays off at time T, where S_T is the stock price at that time. When the stock price follows geometric Brownian motion, it can be shown that its price at time has the form

where S is the stock price at time t and h is a function only of t and T.

(a) By substituting into the Black-Scholes-Merton partial differential equation, derive an ordinary differential equation satisfied by h(t, T).

(b) What is the boundary condition for the differential equation for h(t, T)?

where r is the risk-free interest rate and σ is the stock price volatility.

Reference no: EM131237515

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