美式期权提前行权

对无分红股票的美式看涨期权，通常不应提前行权。

原因是：继续持有期权保留上涨收益，同时不用提前支付执行价 $K$；若利率非负，推迟支付 $K$ 本身有价值，提前行权还会损失剩余时间价值。因此到期前一般有

$$C_t>S_t-K,$$

提前行权被继续持有支配。

对美式看跌期权，提前行权可能最优。若 put 深度实值，提前行权可以立刻收到 $K-S_t$，相当于更早拿到现金并获得利息；此时剩余下跌期权价值可能很小。因此深度实值、高利率等情形下，美式 put 可能提前行权。

若标的有分红，美式 call 也可能在除息日前提前行权。

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英文解析

For a non-dividend-paying stock, it is not optimal to exercise an American call early.

One no-arbitrage argument is to compare the call with immediate exercise. Holding the call preserves upside and keeps the strike $K$ unpaid until exercise. With nonnegative interest rates, delaying payment of $K$ is valuable, and early exercise also destroys remaining time value. Thus

$$C_t>S_t-K$$

before maturity, so exercising the call early is dominated.

For an American put, early exercise can be optimal. If the put is deep in the money, exercising gives $K-S_t$ immediately; receiving $K$ early can earn interest, while the remaining downside optionality may be small. Hence early exercise is possible for puts, especially when rates are high and the option is deep in the money.

If the stock pays dividends, an American call can sometimes be exercised just before an ex-dividend date.