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Put spread too wide for the strike gap

Question

A stock is at 1414. A put struck at 1717 costs 5.95.9, a put struck at 1414 costs 2.12.1 (same expiry), and a bond paying 11 at expiry costs 0.90.9. Find an arbitrage and report the sum of positions in the order (stock) + (17-strike puts) + (14-strike puts) + (bonds), with shorts negative.

Short answer

33. The payoff gap between the two puts never exceeds the strike gap 33, so their price gap must be at most 3×0.9=2.73\times0.9=2.7, yet it is 3.83.8. Sell the 1717 put, buy the 1414 put and buy 33 bonds, collecting 1.11.1 up front with a non-negative payoff: 0−1+1+3=30-1+1+3=3.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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