Maximum Likelihood Estimation of Continuous-time Diffusion Models for Exchange Rates

27 Pages Posted: 17 Apr 2020 Last revised: 24 Apr 2020

See all articles by Seungmoon Choi

Seungmoon Choi

School of Economics, University of Seoul

Jaebum Lee

Independent

Date Written: March 30, 2020

Abstract

Five diffusion models are estimated using three different foreign exchange rates to find an appropriate model for each. Daily spot exchange rates expressed as the prices of 1 euro, 1 British pound and 100 Japanese yen in US dollars, respectively denoted by USD/EUR, USD/GBP, and USD/100JPY, are used. The maximum likelihood estimation method is implemented after deriving an approximate log-transition density function (log-TDF) of the diffusion processes because the true log-TDF is unknown. Of the five models, the most general model is the best fit for the USD/GBP, and USD/100JPY exchange rates, but it is not the case for the case of USD/EUR. Although we could not find any evidence of the mean-reverting property for the USD/EUR exchange rate, the USD/GBP, and USD/ 100JPY exchange rates show the mean-reversion behavior. Interestingly, the volatility function of the USD/EUR exchange rate is increasing in the exchange rate while the volatility functions of the USD/GBP and USD/100Yen exchange rates have a U-shape. Our results reveal that more care has to be taken when determining a diffusion model for the exchange rate. The results also imply that we may have to use a more general diffusion model than those proposed in the literature when developing economic theories for the behavior of the exchange rate and pricing foreign currency options or derivatives.

Keywords: Foreign Exchange Rate, Diffusion Model, Maximum Likelihood Estimation, US Dollar, Euro, British Pound, Japanese Yen

JEL Classification: C22, C51, F31, G15

Suggested Citation

Choi, Seungmoon and Lee, Jaebum, Maximum Likelihood Estimation of Continuous-time Diffusion Models for Exchange Rates (March 30, 2020). East Asian Economic Review, Vol. 24, No. 1, (March 2020) , Available at SSRN: https://ssrn.com/abstract=3577328 or http://dx.doi.org/10.2139/ssrn.3577328

Seungmoon Choi (Contact Author)

School of Economics, University of Seoul ( email )

Seoul, 130-743
Korea

Jaebum Lee

Independent ( email )

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