American options pricing and Interpolation

以內插法加速美式選擇權的評價

Abstract
Pricing European and American options accurately and efficiently has been a main
concern in many studies. Although the closed-form solution of the European option
has already been derived by Fischer Black, Myron Scholes, and Robert Merton and
efficient numerical approximation algorithms are available, there are numerical meth-ods
that price such options with a much smaller cost and within acceptable error
bounds by use of some precomputation.
In the thesis, the method is proposed to build a look-up table for European and
American option values by precomputation. Once this is done, the requested option
value is then interpolated from the table via polynomial interpolation or cubic spline.
Though it takes time to build up the table, since the calculation is done off-line
and once and for all, the cost is fixed and can be amortized. More importantly, the
interpolated option value can be calculated very fast.