市場狀態連動跳躍風險下外匯選擇權之評價與實證分析

Theoretical Valuation and Empirical Analysis of Currency Options Pricing under Jump Risks driven by Market States

莊明哲(Ming-Che Chuang) ； 吳安琪(An-Chi Wu) ； 林士貴(Shih-Kuei Lin) ； 王詩韻(Shin-Yun Wang)

《風險管理學報》 17卷2期 (2015/12) Pp. 145-184

摘要

本文檢視跳躍風險於匯率動態行為的描繪，並應用在匯率選擇權評價模式。研究考量匯率價格連續性波動具升貶循環狀態變化的叢聚特性，並延伸馬可夫狀態轉換機制於間斷性價格跳躍風險上作調控設定，使跳躍頻率與跳躍大小亦隨循環狀態改變而產生相依性。針對主要六種通貨相對美元計價貨幣－歐元、英鎊、日圓、瑞士法郎、加幣與澳幣－於2004年至2014年日資料作為觀察對象與研究期間，並運用EM演算法作參數估計。本文研究發現，跳躍風險具狀態相依的馬可夫調控模型(MS-MMDJ)相對風險獨立跳躍模型能捕捉到較佳的匯率變動情境。進一步利用匯率選擇權資料評估模型之穩建性，結果顯示MS-MMDJ亦能在選擇權資料上有效減少定價誤差，說明納入狀態轉換於跳躍風險對外匯選擇權定價與預測的重要性。

關鍵字

匯率波動 ； 跳躍風險 ； 狀態相依 ； 馬可夫調控模型 ； 選擇權評價

並列摘要

In this article, we investigate currency jump risk behavior and apply to pricing the currency options. We consider six major currencies (EUR, GBP, JPY, CHF, CAD, and AUD) against the USD over the 2004 to 2014 period, and extend the state-dependent into jump risk in a Markov-modulated jump diffusion model, to investigate whether the states of the jump risks have an impact on the jump frequency and the jump size. In the empirical result, we find that the Markov-modulated jump diffusion model with state-dependent jump frequencies and jump sizes (MS-MMDJ) can be more suitable for in the sample observations with six major currencies by expectation-maximization gradient algorithm. Overall, incorporating state-dependent in volatility and jumps is important for pricing and forecasting.

並列關鍵字

exchange rate volatility ； jump risk ； state-dependent ； Markov-modulated model ； currency options pricing

參考文獻

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