4.7. Exercise This problem gives an alternative derivation of the put-call parity when the stock price...

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4.7. Exercise This problem gives an alternative derivation of the put-call parity when the stock price dynamics are given by the Black-Scholes model. Assume that there exists a unique solution of the final value problem (2), i.e. if v = v(t, x) and v2 = v2(t, x) are solu- tions of the PDE in (2) and such that then V(T, x)=v2(T, x), x>0, V(t, x)=v2(t, x), x>0, 0t 0. (iii) By uniqueness, it follows that "(t, x)+x-Ker(T-1) call(t, x) = v(t, x) = v(t, x) = yput ( for all x > 0 and 0t 4.7. Exercise This problem gives an alternative derivation of the put-call parity when the stock price dynamics are given by the Black-Scholes model. Assume that there exists a unique solution of the final value problem (2), i.e. if v = v(t, x) and v2 = v2(t, x) are solu- tions of the PDE in (2) and such that then V(T, x)=v2(T, x), x>0, V(t, x)=v2(t, x), x>0, 0t 0. (iii) By uniqueness, it follows that "(t, x)+x-Ker(T-1) call(t, x) = v(t, x) = v(t, x) = yput ( for all x > 0 and 0t