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> A financial derivative pays out an amount bsn at time T, where S is...

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> A financial derivative pays out an amount bsn at time T, where S is the value of a share, b a constant and n a positive integer. Assuming that, = V(S,t) = A(t).SM is a solution of the Black-Scholes equation, determine the ordinary differential equation that A(t) satisfies. State the boundary condition that A(t) must satisfy to produce the stated pay out of the financial derivative at t=T. - Solve the ordinary differential equation for At), to find an expression for the value of the financial derivative V at time t before expiry, T. > A financial derivative pays out an amount bsn at time T, where S is the value of a share, b a constant and n a positive integer. Assuming that, = V(S,t) = A(t).SM is a solution of the Black-Scholes equation, determine the ordinary differential equation that A(t) satisfies. State the boundary condition that A(t) must satisfy to produce the stated pay out of the financial derivative at t=T. - Solve the ordinary differential equation for At), to find an expression for the value of the financial derivative V at time t before expiry, T

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