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Mispriced straddle against a call and a put

Question

All options below expire at the same date TT with strike K=17K=17. A straddle costs V0=5.4V_0=5.4, a European put costs P0=4.2P_0=4.2 and a European call costs C0=1.4C_0=1.4. The stock trades at S0=14S_0=14 and a zero-coupon bond paying 11 at TT costs B0=0.9B_0=0.9. Construct the arbitrage and report the sum of the holdings in the order (stock) + (call) + (put) + (bonds) + (straddle), with short positions negative.

Short answer

−1-1. A straddle is exactly one call plus one put, which together cost 5.65.6, but the straddle sells for 5.45.4. Buy the straddle and sell the call and the put for a 0.20.2 credit with offsetting payoffs; stock and bonds are not needed, so the sum is 0−1−1+0+1=−10-1-1+0+1=-1.

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

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