A Nonlinear Analysis of Forward Premium and Volatility

Chiente Hsu and Peter Kugler
Department of Economics
University of Bern

Pages 187-201

Abstract

In this paper we investigate the relationship between risk premium and a time-varying conditional variance of spot rate using weekly Swiss franc/US dollar exchange-rate data. First, we apply an EGARCH-in-mean framework to test the unbiasedness hypothesis of the forward rate with a volatility dependent risk premium. The corresponding estimates point to no significant influence of volatility on the risk premium, and reject the unbiasedness hypothesis. Second, we apply a seminonparametric, nonlinear impulse-response analysis to the spot-rate change and the forward premium. This framework allows us to analyze the risk premium/volatility relationship without using a specific, parametric model such as EGARCH-in-mean. The latter analysis confirms the negative EGARCH-in-mean results with respect to the risk premium/volatility relationship, although the volatility dynamics estimated is clearly different from that implied by the EGARCH estimate. Moreover, the forward premium has a nonlinear dynamic influence on the spot rate, whereas the converse is not true.

Bibliography

Bekaert, G., and R. J. Hodrick (1993). "On biases in the measurement of foreign exchange risk premiums." Journal of International Money and Finance, 12: 115-138.
Bollerslev, T., R. Y. Chou, and K. F. Kroner (1992). "ARCH modeling in finance: a review of the theory and empirical evidence." Journal of Econometrics, 52: 5-59.
Domowitz, I., and C. Hakkio (1985). "Conditional variance and the risk premium in a foreign exchange market." Journal of International Economics, 19: 47-66.
Engle, R., D. Lilien, and R. Robins (1987). "Estimating time varying risk premium in the term structure: the ARCH-M model." Econometrica, 55(2): 391-407.
Fama, E. (1984). "Forward and spot exchange rates." Journal of Monetary Economics, 14: 319-338.
Gallant, R., and Douglas W. Nychka (1987). "Semi-nonparametric maximum likelihood estimation." Econometrica, 55(2): 363-390.
Gallant, R., P. Rossi, and G. Tauchen (1993). "Nonlinear dynamic structures." Econometrica, 61: 871-907.
Gallant, R., and G. Tauchen (1989). "Seminonparametric estimation of conditionally constrained heterogeneous processes: asset pricing applications." Econometrica, 57: 1091-1120.
Gallant, R., and G. Tauchen (1992). "A nonparametric approach to nonlinear time series analysis: estimation and simulation." In D. Brillinger, P. Caines, J. Geweke, E. Parzen, M. Rosenblatt, and M. S. Taqqu (eds.), New Directions in Time Series Analysis, part II. New York, NY: Springer-Verlag, pp. 71-92.
Kendall, J. D., and A. D. McDonald (1989). "Univariate GARCH-M and the risk premium in a foreign exchange market." Unpublished manuscript. Department of Economics, University of Tasmania, Hobart.
Lampietti, D. (1993). "Linear versus nonlinear models for exchange rates." Doctoral thesis, University of Bern.
Nelson, D. B. (1990). "Conditional heteroskedasticity in asset returns: a new approach." Econometrica, 59: 347-370.
Pagan, A. R., and A. Ullah (1988). "The econometric analysis of models with risk terms." Journal of Applied Econometrics, 3: 87-105.