多項式無母數選擇權評價模型

Abstract

Cox, Ross, 和 Rubinstein (C.R.R.) 在 1979 年提出一個架構在間斷時間上的二項式評價模型。他們假設股價在各離散時間點上會滿足二項式流程，且其漲幅與跌幅是兩個固定的參數。而事實上，漲跌不單只是固定的比例。本篇論文的主要目的在將 C.R.R. 的二項式評價模型延伸至多項式的情況。並藉由樹狀圖及分割定義域的方法，將股價視為一無母數的隨機變數。

Cox, Ross and Rubinstein (C.R.R. 1979) suggested a Binomial discrete-timemodel for valuing options.They developed the approachby assuming that the stock price follows a multiplicative binomial process over discrete periods.In their procedure, the up(u) and down(d) parameters are regarded as fixed positions which is not realistic. The purpose of this paper is to extend the binomial option-pricing model of C.R.R. to multinomial case where the stock price is treated as a nonparametric random variable over each period. To make this possible, we divide the range of the stock price into finite intervals, and develop our model by a procedure of the multinomial tree.