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

杜化宇(Anthony H. Tu) ； 任紀為(Chi-Wei Jen)

《風險管理學報》 7卷3期 (2005/11) Pp. 237-277

https://doi.org/10.30003/JRM.200511.0002

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Predictive option pricing ； Markov-chain Monte Carlo ； Regime-switching volatility ； Gibbs sampling ； Volatility smile

參考文獻

Amin, K.,Jarrow, R.A.(1991).Pricing Foreign Currency Options under Stochastic Interest Rates.Journal of International Money and Finance.10,310-329.

Working Paper

Bates, D.S.(2000).Post-'87 Crash Fears in S&P500 Futures Option Market.Journal of Econometrics.94,181-238.

Bauwens, L.,Lubrano, M.(1998).Bayesian inference on GARCH models using the Gibbs sampler.Econometrics Journal.1,23-46.

Bauwens, L.,Lubrano, M.(2002).Bayesian Option Pricing Using Asymmetric GARCH Models.Journal of Empirical Finance.9,321-342.