Dynamic Analyzing and Option Pricing of G-10 Exchange Rates:Empirical Results in Markov-Modulated Models

本論文主要目的在探討外匯市場跳躍風險的動態過程，並應用於外匯選擇權評價上。其考量跳躍風險具狀態相依的馬可夫調控的跳躍擴散（MS-MJ）模型，使市場狀態不僅連結報酬波動程度，亦與跳躍大小和跳躍頻率相關，作為捕捉匯率週期性的轉換和異常衝擊下的跳躍特性。本研究以G-10國家貨幣（歐元，英鎊，日圓，加拿大幣，瑞士法郎，澳幣，紐西蘭幣，挪威克朗和瑞典克朗）兌美元的匯率資料作為研究對象，實證結果發現，G-10國家匯率受景氣週期和狀態相關的跳躍風險特性。此外，本研究實證結果顯示，其在大多數G-10國家的外匯市場的動態過程中，MS-MJ模型能相對其他模型適合觀察其狀態轉換下跳躍相依的特性，並能提高大部分G-10國家外匯選擇權在價平定價的有效性。總合而言，納入市場狀態於波動性和跳躍風險能有助於提高模型的配適性和選擇權評價的資訊掌握。This thesis aims to investigate the dynamic process of currency jump risks and applies it to pricing currency options. We explore a Markov-modulated jump diffusion model with state-dependent jump risks (MS-MJ model), which incorporates jump intensity and state-dependence to capture the characteristics of cyclical movements and abnormal shock. Comparing the G-10 currencies (EUR, GBP, JPY, CAD, CHF, AUD, NOK, NZD and SEK) against the USD, the empirical results found that the G-10 currencies are characterized by business cycles and state-dependent jump risks. Moreover, our findings suggest that incorporating state-dependence in jump risks can improve model fitting and option pricing. The sample observations show the MS-MJ model can be more suitable with most of the G-10 spot FX rates, and can improve the pricing performance on most of the G-10 currency options, in particular for at-the-money options