Straddle arbitrage with calls, stock and bonds only
Question
A straddle struck at costs , and a European call with the same strike and expiry costs . No put is traded. The stock is at , and a bond paying at expiry costs . Find the arbitrage and give the total of the positions in the order (stock) + (calls) + (bonds) + (straddles), shorts counted as negative.
Short answer
. By put–call parity a put equals , so a straddle replicates as , costing , far below . Sell the straddle and buy the replica (two calls, short one share, bonds): .
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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