模糊三項式樹狀選擇權評價模型

Fuzzy Trinomial Tree Option Pricing Model

呂正東(Cheng-Tong Lu) ； 溫淑戀(Shu-Lien Wen) ； 李賢哲(Hsien-Che Lee)

《大同大學通識教育年報》 2期 (2006/01) Pp. 291-325

https://doi.org/10.6514/TJGE.200601_(2).0014

摘要

選擇權是一種投資人經常用來套利及避險的工具。目前較為大眾所使用的不外乎是Black-Scholes及CRR模型，但僅能提供一種理論性的參考值，雖經余尚恩（2002）把模糊理論的概念整合到CRR模型上，把股價向＂Up＂及＂Down＂跳動的波動度予以模糊化，而建構了模糊二項式樹狀評價模型。然而依模糊二項式樹狀評價模型所推出的三角模糊數與真實的市場價格仍有相當的差距，與一般傳統的評價模型一樣可歸因於系統性偏差，本文以余尚恩的模糊二項式樹狀評價模型為基礎，增加考量股價向＂Horizontal＂跳動的波動度並予以模糊化，建構模糊三項式樹狀評價模型而模擬計算之，並探究其所產生的三角模糊數是否近似於真實的市場價格。本文的結果發現，當增加考量股價向＂Horizontal＂跳動的波動度並予以模糊化後，其模擬計算所產生的三角模糊數較模糊二項式樹狀評價模型更能接近真實的市場價格，並明顯改善了系統性偏差，並可提供較合理的選擇權價值範圍供各類型的風險投資者做擬定投資策略參考之用。

關鍵字

模糊 ； 波動度 ； 敏感度分析

並列摘要

Option is one of the tools used by investors for arbitrage and hedging. Currently, Black-Scholes and CRR models are commonly used for option pricing. However, they can only provide a theoretical reference. Though Yu (2002) has integrated the concept of fuzzy theory into CRR model to establish Fuzzy Binomial Tree Option Pricing Model (FBTOPM), which fuzzified the ＂Up＂ and ＂Down＂ jumping of stock prices, there is still a gap between the ＂triangular fuzzy number＂ derived from FBTOPM and the market actual price. Like conventional pricing models, FBTOPM is also attributed to system bias. Based on Yu's FBTOPM, this paper intends to take into consideration the volatility of ＂Horizontal＂ jumping of stock prices and to fuzzify that volatility by establishing Fuzzy Trinomial Tree Option Pricing Model (FTTOPM) with a hope to see if the triangular fuzzy number derived from this model can approach to the market actual price. This paper found that taking into consideration the volatility ＂Horizontal＂ of stock prices in the model can substantially improve the problem of system bias and derive a triangular fuzzy number that is closer to the market actual price. In addition, this FTTOPM provides a more suitable option pricing for different risk preference as investment strategy references.

並列關鍵字

Fuzzy ； Volatility ； Sensitivity Analysis