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

• Main Authors: Seungmoon Choi, Jaebum Lee
• Format: Article
• Language: English
• Published: Korea Institute for International Economic Policy 2020-03-01
• Series: East Asian Economic Review
• Subjects: foreign exchange rate; diffusion model; maximum likelihood estimation; us dollar; euro; british pound; japanese yen
• Online Access: http://dx.doi.org/10.11644/KIEP.EAER.2020.24.1.372

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.