台灣認購權證評價之研究－探討二項式及三項式樹狀模型之評價差異

Abstract

本研究的目的主要是透過三種選擇權評價模型，即B-S模型、二項式樹狀模型及三項式樹狀模型，搭配歷史波動率及隱含波動率來對台灣之認購權證作評價，期能找出較適合台灣市場的評價模型與方法。此外，亦對樹狀模型的分割期數作探討，以藉此了解不同分割期數在評價權證上是否有所不同。 研究結果發現，以歷史波動率來評價權證會產生明顯低估的現象，而以隱含波動率來評價權證則能獲得較佳的績效，其中以B-S模型搭配隱含波動率有最佳的評價績效。而在歷史波動率下，不同分割期數的樹狀模型並無規則的評價表現；但若採隱含波動率，則分割期數愈大會有愈佳的評價能力，且三項式樹狀模型評價能力會優於二項式樹狀模型。此外，在隱含波動率下，當權證處於價外時，各模型的評價誤差會比處於價內時還低。

This study adopts three option pricing models ( Black-Scholes model, binomial trees model and trinomial trees model ) with the historical volatility and the implied volatility to price the Taiwan call warrants. We hope to find out the pricing model that is fitting in with Taiwan warrants market. In addition, we study the number of time steps of trees models to understand the pricing outcomes of different number of time steps. The findings are as follows : All pricing models with the historical volatility underestimate warrants obviously, but they obtain a better pricing performance with the implied volatility. Black-Scholes model with the implied volatility is the best pricing model and having the best pricing performance. Using the historical volatility, trees models of different number of time steps have not a regular pricing performance; But using the implied volatility, trees models have a better pricing performance when the number of time steps is bigger, and trinomial trees model is better than binomial trees model.