考慮流動性因素下金融機構發行選擇權之訂價與避險：理論與實證分析

Abstract

本文主旨在考慮流動性因素的選擇權訂價模型與BS訂價模型，來為台灣單一個股之美式認購權證作訂價與避險分析。在證券市場可能存在流動性不足的情況下，本文探討流動性對認購權證的影響，並提出一個數值方法來求解非線性偏微分方程，獲得權證價格及希臘字母(Greeks)並比較其受流動性影響的變化。實證部份比較兩種模型的定價誤差，以及探討何種模型的避險效果較佳：採用三種避險區間來做比較，分別為每日調整、每五日調整與每十日調整避險部位，最後使用無母數檢定來驗證Frey模型避險誤差是否小於BS模型避險誤差，檢驗Frey模型是否適用於台灣市場。研究結果顯示在證券市場可能發生流動性不足的情況下，與BS模型比較，用Frey模型來評價認購權證與避險操作似乎可得到較好的結果。

This paper considers the option pricing model under illiquidity and compares the model to BS model. After solving the nonlinear partial differential equation by a new numerical method, we can observe that how the call warrant prices and Greeks change due to the illiquidity in the underlying asset market. We compare the pricing error of call warrant and hedging strategies of Frey model to those of the standard BS model in Taiwan’s stock market with the illiquidity problems. In order to compare the hedging strategies between the two models, we choose three rebalance intervals. We rebalance the replication of call warrants every day, every five days, and every ten days and conduct nonparametric test to examine that the tracking error in Frey model is less than the tracking error in BS model. According to our results, Frey model is better in Taiwan warrant market with illiquidity.