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U NIVERSITY OF E SSEX D EPARTMENT OF E CONOMICS EC372 Economics of Bond and Derivatives Markets American and European Put Option Premiums This note seeks to clarify why the price (premium) of an American put option almost always exceeds that of a European put option, even in frictionless markets. 1 Let P t and p t denote the respective prices of American and European put options on the same asset, with exercise price X , expiring at date T , where t < T . Remember that P t = p t for all t < T : the opportunity to exercise the American option before T could never negative value (because the only difference between the American and European styles is that the American option could be exercised early, an opportunity that is not available for the European option). Suppose, then, that P t = p t , at some date t < T . 2 Consider the strategy: “write one European put and buy one American put”. Given that P t = p t , the outlay is zero. The payoff on this strategy is never negative and could be positive: hence it is an arbitrage opportunity.
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