Let M = (B, S) be a generic complete and arbitrage-free model where B is the...

 

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Let M = (B, S) be a generic complete and arbitrage-free model where B is the money market account and S is the stock price. We consider a contingent claim X = h(ST) with maturity T and we assume that the payoff function h: R+ → R is twice continuously differentiable. Using integration by parts formula, show that for arbitrary x, y E R+ h(x) — h(y) = h'(y)(x − y) + f ( - -00 (u-x)+h" (u)du + S (x-u)+h" (u) du Let M = (B, S) be a generic complete and arbitrage-free model where B is the money market account and S is the stock price. We consider a contingent claim X = h(ST) with maturity T and we assume that the payoff function h: R+ → R is twice continuously differentiable. Using integration by parts formula, show that for arbitrary x, y E R+ h(x) — h(y) = h'(y)(x − y) + f ( - -00 (u-x)+h" (u)du + S (x-u)+h" (u) du

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To prove the given equation using integration by parts well start with the integration by parts form... View the full answer