考慮流動性下之選擇權訂價模型: 非線性拋物線偏微分方程式的數值方法應用

Abstract

本篇論文提出一個在市場流動性不足情況發生時的選擇權訂價模型，並且發展一個新的數值方法來求解一個非線性拋物線型態的偏微分方程式，同時利用湯馬斯演算法來提升數值運算的效率。在實證研究的部份，我們使用美國的個股選擇權資料來進行分析，首先運用非線性最小平方法來估計標的物的市場流動性，並針對Black-Scholes與本文所運用的模型即Frey模型兩者之間對選擇權定價的損失函數分析。

This paper considers the pricing model of options under illiquidity. A new numerical procedure for solving the nonlinear parabolic partial differential equation is explored and the Thomas algorithm is used to improving the efficiency of the numerical scheme. Using CBOE stock options, we employ the nonlinear least square method for obtaining the liquidity parameter of the underlying stock option in empirical work and then comparing the loss function between the Black-Scholes model and the model which is proposed by Frey and Patie (2001) and will be abbreviated as the Frey model in this paper.