| Summary: | 碩士 === 輔仁大學 === 金融研究所 === 89 === Abstract
This article proposes a new numerical algorithm for American option, adopting the concept of Broadie and Glasserman [1997]. For the reason that there is no unbiased simulation estimator of American option values, we use the confidence intervals that are generated by two estimates, one biased high and the other biased low, of assets price based on random samples of future state trajectories, and these confidence intervals would cover the correct option values.
This article implements the ideal of finite difference method which uses the grid points to replace the whole tree model, and integrates the branches structure of the tree system. Combining finite difference method with tree model, simulation time can be shortened substantially. We obtain close results, and evaluate American option successfully. At the same time, we can compute the option prices of all the gird points, which is distinguishable from other usual simulation tree obtaining only one option price. For path-dependent American option, we adopt the nature of time reverse of Brownian motion to overcome this problem.
However, the key point of accuracy is the exploitation of interpolation. If we use two-point interpolation, the numerical results show a potential error caused by approximation. Moreover, this error will accumulate in backward-simulation process, and cause high and low estimates increase abnormally. This property also influences the accuracy of confidence intervals and point estimates. Especially after adopting common random number, although it can shorten simulation time dramatically, it also makes the error from two-point interpolation accumulate over time. If we change two-point interpolation into cubic spline interpolation, we can improve preceding error and our model can accommodate both speed and accuracy.
|
|---|
