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

Author

Listed:
  • Choi, Seungmoon

    (University of Seoul)

  • Lee, Jaebum

    (University of Seoul)

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.

Suggested Citation

  • Choi, Seungmoon & Lee, Jaebum, 2020. "Maximum Likelihood Estimation of Continuous-time Diffusion Models for Exchange Rates," East Asian Economic Review, Korea Institute for International Economic Policy, vol. 24(1), pages 61-87, March.
    • Handle: RePEc:ris:eaerev:0372
    DOI: 10.11644/KIEP.EAER.2020.24.1.372
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    More about this item

    Keywords

    Foreign Exchange Rate; Diffusion Model; Maximum Likelihood Estimation; US Dollar; Euro; British Pound; Japanese Yen;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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