Put–call parity arbitrage

MediumFinance & Derivatives~5m

A stock is at $100 (no dividends), $r=5\%$ continuous, $T=1$ year. A $100-strike European call trades at $8 and the $100-strike put at $5. These quotes violate put–call parity, so a riskless arbitrage exists. What profit (in dollars, to two decimals) can you lock in per share, banked today?

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Compare the synthetic forward $C-P$ with $S-Ke^{-rT}$ .
Arb $=(S-Ke^{-rT})-(C-P)=(100-100e^{-0.05})-(8-5)$ .

Answer

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1.88 (± 0.02)

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Put–call parity arbitrage

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