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


Date Written: March 30, 2020


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: or

Seungmoon Choi (Contact Author)

School of Economics, University of Seoul ( email )

Seoul, 130-743

Jaebum Lee

Independent ( email )

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