American Versus European Call

Key idea. An American call gives every right the European call gives, plus the right to exercise early. So $C^{\mathrm{Am}}\ge C^{\mathrm{Eu}}$ must hold. Here $3.15<3.21$, which violates this.

Strategy. Today, buy the American call for $3.15$ and sell the European call for $3.21$. This brings in a credit of $3.21-3.15=0.06$.

Hold the American call to expiry and never exercise it early. The European call we sold can only be exercised at $T$. At $T$ the two positions pay

in every state of the world. We are long the American, so the counterparty can never exercise against us early. The $0.06$ is therefore kept with no risk and no further cash flows.

Remark. The quotes break a second bound as well. For a call on a non-dividend-paying stock, $C\ge S_0-KZ_0=24-21(0.9)=5.10$, and both quotes are below this. Buying the American call, shorting one share and buying $21$ bonds brings in

today. At $T$ this position pays $(S_T-K)^+-S_T+K=(K-S_T)^+\ge0$. So the arbitrage is not unique. As for the two calls, since both are on a non-dividend-paying stock, their fair values should in fact be equal.