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Derivation of the closed-form formulas for European options Let DT = max(0, ST – K) be the payoff of a European call with strike K and maturity T. The following questions provide a step-by-step derivation of the closed-form formulas for c0 and p0 in the lognormal model.
(a) Show that where and otherwise.
(b) Show that ST has the same distribution as
(c) Show that Y > K if and only if .
(d) Using the change of variable show that .
(e) Establish the closed-form formulas for c0 and p0.
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