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European call priced above its American twin

Question

A non-dividend-paying stock trades at 2424. Two calls with strike 2121 and the same expiry are available: a European one at 3.213.21 and an American one at 3.153.15. A bond paying 11 at expiry costs 0.90.9. If an arbitrage exists, what up-front credit does it lock in (two decimals)? Answer −1-1 if there is none.

Short answer

0.060.06. An American call can never be worth less than its European counterpart, and with no dividends it is never optimal to exercise early. Sell the European call at 3.213.21, buy the American at 3.153.15, and hold the American to expiry so the payoffs cancel, keeping 0.060.06.

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

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