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Straddle arbitrage with calls, stock and bonds only

Question

A straddle struck at K=15K=15 costs V0=3.2V_0=3.2, and a European call with the same strike and expiry costs C0=2.3C_0=2.3. No put is traded. The stock is at S0=17S_0=17, and a bond paying 11 at expiry costs B0=0.9B_0=0.9. Find the arbitrage and give the total of the positions in the order (stock) + (calls) + (bonds) + (straddles), shorts counted as negative.

Short answer

1515. By put–call parity a put equals C−S+KBC-S+KB, so a straddle replicates as 2C−S+15B2C-S+15B, costing 4.6−17+13.5=1.14.6-17+13.5=1.1, far below 3.23.2. Sell the straddle and buy the replica (two calls, short one share, 1515 bonds): −1+2+15−1=15-1+2+15-1=15.

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

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