台灣黃金選擇權之訂價模型—隨機短利模型

The Pricing Model of Taiwanese Gold Option with the Short-Rate Model

謝岱桓(Tai-Huan Hsieh)

指導教授 ： 湯美玲

國立虎尾科技大學/管理學院/財務金融系碩士班/碩士(2016年)

摘要

根據台灣黃金選擇權所定義的標的資產，其中會遭遇到匯率風險，這代表了其定價模式應參照Quanto選擇權，除此之外，其標的物價格應不為標準布朗運動，無風險利率假設為常數也有待商榷，在本研究中有兩模型，並試圖完成下列三個研究目的：
一、 在第一個模型下，對標的物價格變動過程擬定為Ornstein – Uhlenbeck模型，並將之帶入Quanto選擇權，利用平賭方法訂價。
二、 第二個模型則加入短利模型，並以國庫券價格來代替利率。
三、 比較兩者的差異，並利用VBA程式進行模擬，將結果顯示出來。
模擬結果可以發現新模型利用隨機利率模擬國庫券價格時，與市場結算價相去不遠。

關鍵字

平賭方法 ； Black – Scholes選擇權評價模型 ； 短期利率模型

並列摘要

According to the underlying asset of Taiwanese Gold Option (TGO), the TGO price will encounter currency risk. It means that the payoff function is similar as Quanto option. Generally speaking, the stochastic process of Quanto option’s underlying asset is assumed to follow a standard Brownian motion, and its’ interest rate is assumed to be constant. These assumptions are unsuitable. To improve the TGO pricing model, this paper has three purposes as follow:
1. To develop the first model, the stochastic process of logarithm gold price is assumed to follow Ornstein – Uhlenbeck model. Using the Quanto option model to evaluate this model.
2. The second model increases the other factor, stochastic interest rate, which is assumed to follow Ornstein – Uhlenbeck model. And replace the risk-free rate by Zero Coupon Bond.
3. The first one and second one was compared, and we simulate the price by VBA code.
We found that the price of MTGO model was close with settlement price.

並列關鍵字

Martingale Approach ； Black – Scholes model ； Short-term interest rate model

參考文獻

[1]Bessembinder, H., Coughenour, J. F., Seguin, P. J. and Smoller, M. M.(1995), Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure, The Journal of Finance(1995), 361-375

[3]Boulier, J.F., Huang,S. and Taillard,G.(2001), Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund, Insurance: Mathematics and Economics(2001), 173-189.

[5]Davis, M.H.A.(2006), Mathematical Option Price, Imperial College London

[6]Gibson, R. and Schwartz, E.S.(1990), Stochastic Convenience Yield and the Pricing of Oil Contingent Claims, The Journal of Finance(1990), 959-976

[8]Hull, J.C.(2010), Fundamentals of Futures and Options Marckets(7 edition), PEARSON