Mispriced straddle against a call and a put
Question
All options below expire at the same date with strike . A straddle costs , a European put costs and a European call costs . The stock trades at and a zero-coupon bond paying at costs . Construct the arbitrage and report the sum of the holdings in the order (stock) + (call) + (put) + (bonds) + (straddle), with short positions negative.
Short answer
. A straddle is exactly one call plus one put, which together cost , but the straddle sells for . Buy the straddle and sell the call and the put for a credit with offsetting payoffs; stock and bonds are not needed, so the sum is .
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
See the hint and the full worked solution in the question bank (free account).
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
Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.
Read it free