# American Options on Assets with Dividends Near Expiry

American Options on Assets with Dividends Near Expiry

This Demonstration shows an explicit expression for the optimal exercise boundary of American options on assets with dividends. The function (t) of the optimal exercise boundary is only valid near expiry. The graph shows the (t) curve (green line) near expiry for a three-year maturity option. For the option's holder, it is not optimal to exercise the option while the asset price moves within the colored area.

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The optimal exercise boundary is singular at expiry, and its behavior is a classical problem of mathematical finance. This type of singularity is common in similar free boundary problems in physics, for example, the movement of the boundary between melting ice and water.