Derive a relation between partialctst kpartialk and, Operation Management

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Derive a relation between partialctst kpartialk and

Assume the interest rate is zero and also assume that both call and put options with respective values Ct(St,K) and Pt(St, K) are differentiable functions of the strike K. (a) Derive a relation between partialCt(St, K)/partialK and partialPt(St, K)/partialK for t = 0 and t = T. (b) Find the values of these partial derivatives at maturity t = T.

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