Lecture 9 Tutorial Questions - Solutions.pdf

# Define p 1 p 2 and p 3 as the prices of puts with

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Define p 1 , p 2 and p 3 as the prices of puts with strike prices K 1 , K 2 and K 3 . With the usual notation 1 1 1 rT c K e p S 2 2 2 rT c K e p S 3 3 3 rT c K e p S Hence 1 3 2 1 3 2 1 3 2 2 ( 2 ) 2 rT c c c K K K e p p p Because 2 1 3 2 K K K K , it follows that 1 3 2 2 0 K K K and 1 3 2 1 3 2 2 2 c c c p p p The 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 3 8 2 5 1 \$ initially. The following table shows the profit/loss from the strategy. Stock Price Payoff Profit 65 T S 0 1 60 65 T S 65 T S 64 T S 55 60 T S 55 T S 56 T S 55 T S 0 1 The butterfly spread leads to a loss when the final stock price is greater than \$64 or less than \$56.

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Problem 11.20 There are two alternative profit patterns for part (a). These are shown in Figures S11.2 and S11.3. In Figure S11.2 the long maturity (high strike
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