Valuing Foreign Currency Options with a Mean-Reverting Process: A Study of Hong Kong Dollar

International Journal of Finance & Economic, Vol. 13, pp. 118-134, 2008

17 Pages Posted: 21 Jan 2008 Last revised: 29 Mar 2011

See all articles by Cho-Hoi Hui

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department

Chi-Fai Lo

The Chinese University of Hong Kong

Vincent Yeung

Hong Kong Monetary Authority

Laurence Fung

Hong Kong Monetary Authority

Date Written: May 11, 2008

Abstract

The theoretical prediction on targeted exchange rates expects mean reversion of the exchange rates. There is some empirical evidence to support this prediction. This paper presents a model for valuing European foreign exchange options in which the forward foreign exchange rate follows a mean-reverting lognormal process. The corresponding closed-form solutions for the option valuation are derived. The mean-reverting process has material impact on the foreign exchange rate option values and their hedge parameters. This tends to decrease the value of a simple put or call. On the other hand, the process also keeps the exchange rate in a small range around the mean level. As this is the region in which an option’s intrinsic value is high because of the level of its strike price, there is also a tendency for option values to be enhanced compared with the values of the Black–Scholes model. The numerical results using the forward exchange rates of the Hong Kong dollar and market data of their options show that both of these effects are important for the realistic choices of parameter values. As the dynamics of targeted exchange rates may not follow the standard lognormal process as described by the Black–Scholes model, the mean-reverting option-pricing model may be considered for the valuation of options and estimation of associated hedge parameters on targeted exchange rates.

Keywords: Target foreign exchange rates, currency options, mean-reverting process

JEL Classification: F13, G13

Suggested Citation

Hui, Cho-Hoi and Lo, Chi-Fai and Yeung, Vincent and Fung, Laurence, Valuing Foreign Currency Options with a Mean-Reverting Process: A Study of Hong Kong Dollar (May 11, 2008). International Journal of Finance & Economic, Vol. 13, pp. 118-134, 2008. Available at SSRN: https://ssrn.com/abstract=1085998

Cho-Hoi Hui (Contact Author)

Hong Kong Monetary Authority - Research Department ( email )

Hong Kong
China

Chi-Fai Lo

The Chinese University of Hong Kong ( email )

Department of Physics
Shatin, N.T., Hong Kong
China

Vincent Yeung

Hong Kong Monetary Authority ( email )

3 Garden Road, 30th Floor
Hong Kong
Hong Kong

Laurence Fung

Hong Kong Monetary Authority ( email )

55/F, Two International Finance Centre
8 Finance Street, Central
Hong Kong
Hong Kong

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