UNIVERSITY OFESSEXDEPARTMENT OFECONOMICSEC372 Economics of Bond and Derivatives MarketsAmerican and European Put Option PremiumsThis note seeks to clarify why the price (premium) of an American put option almost alwaysexceeds that of a European put option, even in frictionless markets.1LetPtandptdenote the respective prices of American and European put options onthe same asset, with exercise priceX, expiring at dateT, wheret < T. Remember thatPt=ptfor allt < T: the opportunity to exercise the American option beforeTcould nevernegative value (because the only difference between the American and European styles isthat the American option could be exercised early, an opportunity that is not available forthe European option).Suppose, then, thatPt=pt, at some datet < T.2Consider the strategy: “write oneEuropean put and buy one American put”. Given thatPt=pt, the outlay is zero. The payoffon this strategy is never negative and could be positive: hence it is an arbitrage opportunity.
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