Early Exercise Premium

The early exercise premium is the additional value inherent in an American option compared to a European option, resulting from the holder's right to exercise the contract before expiration. This premium exists because the ability to capture intrinsic value at an optimal moment is a valuable flexibility that the European option lacks.

The magnitude of this premium is influenced by factors such as the proximity to expiration, the volatility of the underlying asset, and any expected cash flows like dividends. For example, if a stock is expected to pay a large dividend, it may be optimal to exercise a call option early to capture that dividend.

The early exercise premium is effectively the price the market pays for the flexibility to terminate the contract early. In trinomial tree models, this premium is calculated by comparing the continuation value of the option at each node with the immediate payoff of exercise, capturing the exact value of this strategic choice.