Put spread too wide for the strike gap
Question
A stock is at . A put struck at costs , a put struck at costs (same expiry), and a bond paying at expiry costs . 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
. The payoff gap between the two puts never exceeds the strike gap , so their price gap must be at most , yet it is . Sell the put, buy the put and buy bonds, collecting up front with a non-negative payoff: .
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- The Law of One Price and Replication: No-Arbitrage Pricing from First Principles
- Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
- Option Trading Strategies: Spreads, Combinations, and Payoff Engineering
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