Tilley's Bundling Algorithm
Tilley's Bundling Algorithm
This Demonstration shows Tilley's bundling algorithm [1] that uses Monte Carlo simulation to approximate the value of an American option on a single underlying asset. The graph shows the simulated geometric Brownian motion (GBM) paths (gray lines), the "transition zone" (dashed lines), and the "sharp boundary" (red dots), which is the algorithm's approximation for the optimal exercise boundary (t) (black line). Whenever a GBM path falls below the "sharp boundary", the early-exercise is considered optimal and the option is instantly exercised. The early-exercise events at each time step are illustrated by the abrupt cut of those GBM paths that fall bellow the red dots. For each GMB path, the intrinsic value of the option at the time of exercise is discounted, and Monte Carlo integration helps to approximate the American put at .
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t=0
Use the controls to set the option's parameters. Observe how the selected number of time steps, bundles, and paths per bundle affect the approximation for the option's value and the early-exercise boundary location. The "seed" control generates new pseudorandom GBM paths.