# Hold-or-Exercise for an American Put Option

Hold-or-Exercise for an American Put Option

This Demonstration shows the "hold-or-exercise" process during the life of an American put option. The early exercise boundary is constructed according to the quadratic approximation analytical method [1]. Pseudorandom geometric Brownian motion (GBM) paths simulate the asset price through time; whenever a path touches the boundary (dashed red line in the upper graph), the option is instantly exercised. For each path, the intrinsic value of the option at the time of exercise is discounted, and Monte Carlo integration helps to estimate the American put at . Use the controls to set the parameters of the option and observe the impact of time discretization and number of GBM paths on the convergence. The more GBM paths, the better the approximation.

t=0