Interpolation and american options pricing

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