Heston隨機波動率模型與NGARCH選擇權定價模型在匯率連動選擇權上之實證比較

An empirical comparison between the Heston stochastic volatility model and the NGARCH model in pricing quanto options

趙祥安(Xiang-An Zhao)

指導教授 ： 鄧惠文 ； 康明軒

國立交通大學/理學院/應用數學系暨研究所/碩士(2020年)

摘要

外匯市場為全球主要的金融市場之一。匯率連動選擇權(Quanto options)正是為一以外國資產為標的物的選擇權。然而與樸素選擇權不同的是，匯率連動選擇權的報酬函數中包含了匯率，依據不同的報酬函數該契約可以有效的幫助國內投資人在投資外國資產時仍可規避外匯風險。由於匯率連動選擇權為一多資產的新奇選擇權，其需要同時考慮到匯率與外國標的物的隨機過程，因此如何準確的評價該類選擇權至今仍在實務上是個困難的問題。相較於Black and Scholes (1973)模型，經實證研究，Heston (1993) 隨機波動率模型與Duan (1995) 異質變異數期權定價模型可以有效增加選擇權的定價的準確率。故本文以Black and Scholes (1973) 模型為基準，探討多維Heston (1993) 隨機波動率模型與Duan and Wei (1999) 模型兩項經典模型在匯率連動選擇權上的定價表現。我們以臺灣期貨交易所之臺幣計價的黃金選擇權為例，並比較模型間樣本內的校準表現，以及其樣本外的定價表現。我們發現雖然兩種模型都可以有效增加定價的準確性，其中以Duan and Wei (1999) 模型表現最佳。

關鍵字

匯率連動選擇權 ； Black-Scholes 模型 ； NGARCH 異質變異數模型 ； Heston 隨機波動率模型 ； 蒙地卡羅模擬 ； 模型驗證

並列摘要

Exchange rate market is one of the largest _nancial markets. A quanto option gives the buyer the right
to buy a foreign asset using domestic currency. Quanto options are appealing to investors, because they allow domestic investors to avoid exchange rate risk. A quanto option can be considered as a multi-asset derivative, and the dynamics of foreign asset and exchange rate should be modelled simultaneously. We take the gold option traded in Taiwan Futures Exchange as an example of quanto options, and investigate the pricing performance between the multivariate stochastic volatility model in Heston (1993) and the multivariate NGARCH model in Duan and Wei (1999). Our empirical studies indicate the GARCH model is preferred in both in-sample and out-of-sample analysis.

並列關鍵字

Quanto options ； Black-Scholes model ； NGARCH model ； Heston stochastic volatility model ； Monte Carlo simulation ； Model validation

參考文獻

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