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Define p1, p2and p3as the prices of puts with strike prices K1, K2and K3. With the usual notation 111rTcK epS222rTcK epS333rTcK epSHence 1321321322(2)2rTcccKKKepppBecause 2132KKKK, it follows that 13220KKKand 13213222cccpppThe cost of a butterfly spread created using European calls is therefore exactly the same as the cost of a butterfly spread created using European puts. Problem 11.19 A butterfly spread is created by buying the $55 put, buying the $65 put and selling two of the $60 puts. This costs 38251$initially. The following table shows the profit/loss from the strategy. Stock Price Payoff Profit 65TS0 16065TS65TS64TS5560TS55TS56TS55TS0 1The butterfly spread leads to a loss when the final stock price is greater than $64 or less than $56.
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