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

Seungmoon Choi and Jaebum Lee ()
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Jaebum Lee: University of Seoul

East Asian Economic Review, 2020, vol. 24, issue 1, 61-87

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 (search for similar items in EconPapers)
JEL-codes: C22 C51 F31 G15 (search for similar items in EconPapers)
Date: 2020
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