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Title:	跳躍風險相關之匯率選擇權: 傅立葉轉換評價法
Authors:	林士貴 Lin, Shih-kuei 莊明哲;温晉祥 Chuang, Ming-che;Wen, Chin-hsiang
Contributors:	金融系
Keywords:	外匯選擇權;相關跳躍風險;匯率;傅立葉轉換;利率 Jarrow and Yildirim model;Currency option;Correlated jump risks;Exchange rate;Generalized Fourier transform;Interest rate
Date:	2019-12
Issue Date:	2022-07-06 10:00:03 (UTC+8)
Abstract:	本研究調查近年來美國、日本、歐盟、英國的利率與匯率的走勢，發現利率與匯率同時發生跳躍情況非常頻繁，因此建立一個考慮布朗運動相關以及跳躍相關的模型來捕捉此特性，稱作CB-CJ（Jarrow and Yildirim model with correlated jump risks）模型。實證結果發現CB-CJ比起GBM（Geometric Brownian model）、CB（Jarrow and Yildirim model）、CB-IJ（Jarrow and Yildirim model with independent jump risks）可以更加捕捉利率及匯率的特性。根據此模型找出平賭條件後，我們利用傳立葉轉換評價法推導出CB-CJ下的匯率選擇權評價公式。本研究加入蒙地卡羅法來驗證傅立葉轉換法所計算出來之評價結果以及計算時間，發現傅立葉評價法計算結果與蒙地卡羅法相當接近，而且計算速度遠快於蒙地卡羅法。另外實證發現，CB-CJ改善了樣本內及樣本外定價誤差，使匯率選擇權評價更爲精確。此結果支持我們認爲的利率、匯率跳躍存在相關性之假設。 In this paper, we investigate dynamic behaviors and jump risks of interest rates and exchange rates for United States (US), Japan (JPN), European Union (EU), and United Kingdom (UK) over the recent decade. Given the characteristics of correlated jump risks in interest rates and exchange rates, we construct a new model called Jarrow and Yildirim model with correlated jump risks (CB-CJ) to capture the movements. The empirical results in exchange rate and interest rate data with the log-likelihood value show that CB-CJ can capture the interest rates and the exchange rates better than Geometric Brownian model (GBM), Jarrow and Yildirim model (CB), and Jarrow and Yildirim model with independent jump risks (CB-IJ). After finding the martingale condition, we derive the pricing formula for currency options under CB-CJ with the generalized Fourier transform. This study adds the Monte Carlo method to verify the evaluation results and compare calculating time. We found that the Fourier evaluation method is very close to the Monte Carlo method, and the calculation speed is much faster than the Monte Carlo method. In addition, the empirical performance of the option data finds that CB-CJ improves the in-sample and out-of-sample pricing error performances in most cases. Therefore, we conclude that correlated jump risks between interest rates and exchange rates play important roles for currency options.
Relation:	中國統計學報, Vol.57, No.4, pp.308-341
Data Type:	article
Appears in Collections:	[Department of Money and Banking] Periodical Articles

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