考慮違約風險與隨機利率模型下的匯率連結外幣資產選擇權定價

Pricing Exchange-rate-Linked Options on Foreign Assets with the Counterparty Default Risk within the HJM Interest Rate Model

吳宥璇(Yu-Hsuan Wu) ； 林士貴(Shih-Kuei Lin) ； 張瑞珍(Jui-Jane Chang)

《中國統計學報》 57卷2期 (2019/06) Pp. 120-157

摘要

匯率衍生性金融商品皆屬於店頭市場（over-the-counter, OTC）交易，且匯率波動與本國及外國之利率有一定的關係，在評價匯率衍生性金融商品時，若忽略交易對手違約風險與利率波動及匯率之相關性，將有失適用性。因此本文延伸有違約風險的匯率選擇權在HJM（Heath, Jarrow and Morton, 1992）遠期利率模型架構下的評價公式，考量上述兩個因子來評價。本研究在信用風險因子的模型設定中，進一步加入HJM遠期利率模型架構，進而求得隨機利率下考慮違約風險之匯率連動選擇權評價模型，以提供投資人來因應匯率風險管理的避險需求。本文將此評價模型應用於最常見的四種匯率連結外幣資產選擇權爲範例，探討其在隨機利率與信用風險下合理的價格。

關鍵字

HJM利率模型 ； 匯率連結外幣資產選擇權 ； 信用風險 ； 衍生性商品定價

並列摘要

Most of foreign currency derivatives are traded in the over-the-counter (OTC) and thus is not equipped with the mechanism of margin account and marking to market. Moreover, the exchange rate is greatly affected by the dynamics of both domestic and foreign interest rates. Therefore, if the foreign currency derivatives are priced without the consideration of the counterparty default risk and interest rate, their pricing may cause some pricing error. To solve this problem, this paper presents a pricing formula for foreign currency options with the consideration of the counterparty default risk and interest rate risks within the HJM interest rate model.

並列關鍵字

credit risk ； derivatives pricing model ； foreign currency derivatives ； HJM interest rate Model

參考文獻

Black, F. and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political and Economy, Vol. 81, 637-659.

Heath, D., Jarrow, R. and Morton, A. (1992). Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.Econometrica,Vol. 60(1), 77-105.

Hilliard, J.E., Madura, J. and Tucker, A.L. (1991). Currency Option Pricing with Stochastic Domestic and Foreign Interest Rates, Journal of Financial and Quantitative Analysis, Vol. 26(2), 139-151.

Hull, J.C. and White, A. (1995). The Impact of Default Risk on the Prices of Options and Other Derivative Securities. Journal of Banking and Finance, Vol. 19, 299-322.

Johnson, H. and Stulz, R. (1987). The Pricing of Options with Default Risk. Journal of Finance, Vol. 42, 267-280.