外匯選擇權的定價與馬可夫鏈蒙地卡羅法的應用

Currency Option Pricing with Markov-Chain Monte-Carlo (MCMC) Applications

10.30003/JRM.200511.0002

杜化宇(Anthony H. Tu)；任紀為(Chi-Wei Jen)

預測選擇權定價 ； 馬可夫鍵蒙地卡羅法 ； 狀態轉換波動 ； 吉普斯抽樣法 ； 笑狀波幅 ； Predictive option pricing ； Markov-chain Monte Carlo ； Regime-switching volatility ； Gibbs sampling ； Volatility smile

風險管理學報

7卷3期（2005 / 11 / 01）

237 - 277

繁體中文

假設匯率在狀態轉換的架構下，本文應用馬可夫鏈蒙地卡羅法來評價歐式外匯選擇權。使用英鎊、瑞士法郎、澳幣及日圓等四國貨幣對美元匯率為例，我們發現傳統Black-Scholes的定價在資產價格遵循狀態轉換的過程下產生明顯的定價誤差。使用貝氏原理與吉普斯抽樣法，本文模型允許狀態轉換模型中的參數可存在隨機性。因此，本文模型可視為先前Bollen（1998）的五元樹的狀態轉換模型的一般化延伸。本文模型所計算出的預測選擇權價格所呈現的波動度微笑型態要比Bollen更接近於先前實証結果。

In this paper, we present a Markov-Chain Monte Carlo (MCMC) simulation method for valuing a European-style currency option in a regime-switching framework of exchange rate. Since the Bayesian inference via Gibbs sampling incorporates uncertainty associated with the underlying parameters of the regime-switching model, Our model generalizes the lattice-based regime-switching model by Bollen (1998). Using the sterling (to US dollar) Swiss franc, Australian dollar and Japanese yen, the Black-Scholes model is shown to generate significant pricing errors when a regime-switching process governs underlying asset returns. The computed predictive option pricing are shown to generate the implied volatility smiles commonly found in earlier empirical studies.

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