呂育道臺灣大學：財務金融學研究所廖士豪Liao, Shi-HauShi-HauLiao2007-11-282018-07-092007-11-282018-07-092004http://ntur.lib.ntu.edu.tw//handle/246246/60849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.1 Introduction 1 2 Backrounds 3 2.1 Derivatives Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Option Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Payoffs on Standard Options . . . . . . . . . . . . . . . . . . . 4 2.2 Pricing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 The Balck-Scholes Formula . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Binomial Option Pricing Model . . . . . . . . . . . . . . . . . 7 3 Polynomial and Cubic Spline Interpolation 9 3.1 Polynomial Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Cubic Spline Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Interpolation in Two or More Dimensions . . . . . . . . . . . . . . . . 13 3.4 Comparison Between Polynomial and Cubic Spline Interpolation . . . 14 3.4.1 Computational complexity . . . . . . . . . . . . . . . . . . . . 14 3.4.2 Polynomial wiggle problem . . . . . . . . . . . . . . . . . . . . 19 4 Numerical Results 22 4.1 Building Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5 Conclusion 32 Bibliography 33260042 bytesapplication/pdfen-US美式選擇權內插American options pricingInterpolationthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/60849/1/ntu-93-R91723055-1.pdf