Analysis of Time Varying Exchange Rate Risk Premia

Part of the Studies in Computational Finance book series (SICF, volume 1)


There is a huge literature on the existence of risk premia in the foreign exchange market and its influence in explaining the divergence between the forward exchange rate and the subsequently realised spot exchange rate. In this paper, we seek to model directly the risk premium as a mean-reverting diffusion process. This is done by making use of the spotforward price relationship and assuming a geometric diffusion process for the spot exchange rate. We are able to obtain a stochastic differential equation system for the spot exchange rate, the forward exchange rate and the risk premium which we estimate using Kaiman filtering techniques. The approach we adopt allows us to use daily observations of forward exchange rates of different maturities. This, in turn, characterises the risk premium over time for different time to maturities, thus obtaining a term structure for the risk premium. We present the results of application of our methodology to the Australian dollar and the British pound, both against the U.S. dollar, for three different maturities of forward exchange rates.

Key words

Arbitrage forward exchange premium market price of risk filtering. 


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  1. Backus, D., A. Gregory and C. Telmer (1993), ‘Accounting for Forward Rates in Markets for Foreign Currency’, Journal of Finance, 48, 1887–1908.CrossRefGoogle Scholar
  2. Baillie, R. and T. Bollerslev (1990), ‘A Multivariate Generalized ARCH Approach to Modelling Risk Premia in Forward Exchange Markets’, Journal of International Money and Finance, 9, 309–324.CrossRefGoogle Scholar
  3. Bakshi, G. S. and A. Naka (1997), ‘Unbiasedness of the Forward Exchange Rates’, The Financial Review, 32(1), 145–162.CrossRefGoogle Scholar
  4. Bekaert, G. (1994), ‘Exchange Rate Volatility and Deviation from Unbiasedness in a Cash-In-Advance Model’, Journal of International Economics, 36, 29–52.CrossRefGoogle Scholar
  5. Bhar, R. and C. Chiarella (1997), ‘Merest Rate Futures: Estimation of Volatility Parameters in an Arbitrage-Free Framework’, Applied Mathematical Finance, 4, 1–19.CrossRefGoogle Scholar
  6. Canova, F. (1991), ‘An Empirical Analysis of Ex Ante Profits from Forward Speculation in Foreign Exchange Markets’, Review of Economics and Statistics, 73, 489–496.CrossRefGoogle Scholar
  7. Canova, F. and T. Ito (1991), ‘The Time Series Properties of the Risk Premium in the Yen/Dollar Exchange Market’, Journal of Applied Econometrics, 6, 125–142.CrossRefGoogle Scholar
  8. Canova, F. and J. Marrinan (1993), ‘Profits, Risk and Uncertainty in Foreign Exchange Markets’, Journal of Monetary Economics, 32, 259–286.CrossRefGoogle Scholar
  9. Cheung, Y. (1993), ‘Exchange Rate Risk Premiums’, Journal of International Money and Finance, 12, 182–194.CrossRefGoogle Scholar
  10. Dunis, C. and A. Keller (1995), ‘Efficiency Tests with Overlapping Data: An Application to the Currency Option Market’, European Journal of Finance, 1, 345–366.CrossRefGoogle Scholar
  11. Engel, C. (1996), ‘The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence’, Journal of Empirical Finance, 3, 123–192.CrossRefGoogle Scholar
  12. Hansen, L. P. and R. J. Hodrick (1980), ‘Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis’, Journal of Political Economy, 88, 829–853.CrossRefGoogle Scholar
  13. Harvey, A. C. (1990), Forecasting Structural Time Series Models and the Kaiman Filter, Cambridge University Press, Cambridge.Google Scholar
  14. Harvey, A., E. Ruiz and N. Shephard (1994), ‘Multivariate Stochastic Variance Models’, Review of Economic Studies, 61, 247–264.CrossRefGoogle Scholar
  15. Hull, J. C. (1997), Options, Futures and Other Derivatives, Third Edition, Prentice Hall International Inc.Google Scholar
  16. Jazwinski, A. H. (1970), Stochastic Processes and Filtering Theory, Academic Press, New York.Google Scholar
  17. Kloeden, P. E. and E. Platen (1992), Numerical Solution of Stochastic Differential Equations, Springer-Verlag.Google Scholar
  18. Phillips, P. C. B. and J. W. McFarland (1997), ‘Forward Exchange Market Unbiasedness: The Case of Australian Dollar Since 1984’, Journal of International Money and Finance, 16, 885–907.CrossRefGoogle Scholar
  19. Stulz, R. (1994), ‘International Portfolio Choice and Asset Pricing: An Integrative Survey’, Working paper No. 4645, NBER, Cambridge, MA.Google Scholar
  20. Wolff, C. C. P. (1987), ‘Forward Foreign Exchange Rates, Expected Spot Rates and Premia: A Signal-Extraction Approach’, The Journal of Finance, 42(2), 395–406.Google Scholar
  21. Wu, Y. and H. Zhang (1997), ‘Forward Premiums as Unbiased Predictors Of Future Currency Depreciation: A Non-Parametric Analysis’, Journal of International Money and Finance, 16, 609–623.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  1. 1.School of Finance & EconomicsUniversity of TechnologySydneyAustralia
  2. 2.University of TechnologySydneyAustralia

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