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An Empirical Examination of the Variance‐Gamma Model for Foreign Currency Options

Elton A. Daal and Dilip B. Madan
The Journal of Business
Vol. 78, No. 6 (November 2005), pp. 2121-2152
DOI: 10.1086/497039
Stable URL: http://www.jstor.org/stable/10.1086/497039
Page Count: 32
Subjects: Finance Business
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Abstract

We apply the variance‐gamma (VG) option‐pricing model to currency options. The model is a pure infinite‐activity jump model. We examine whether and to what extent this new model can improve the pricing quality for currency options over the existing modified Black‐Scholes model and the Merton jump‐diffusion (JD) model. We find that the VG model yields better out‐of‐sample pricing performance than the modified Black‐Scholes model or the JD model. In addition, a cross‐entropy analysis shows that the VG model is more consistent with the general criterion of utility maximization and optimal portfolio selection.

Notes and References

This item contains 24 references.

References
  • ['Akgiray, V., and G. Booth. 1988. Mixed diffusion‐jump process of exchange rate movements. Review of Economics and Statistics 70:631–37.']
  • ['Amari, S. 1985. Differential geometric methods in statistics. Lecture Notes in Statistics 28. Berlin: Springer‐Verlag.']
  • ['Bakshi, G., C. Cao, and Z. Chen. 1997. Empirical performance of alternative option pricing models. Journal of Finance 52:2003–49.']
  • ['Bakshi, G., and D. Madan. 2000. Spanning and derivative security valuation. Journal of Financial Economics 55:205–38.']
  • ["Bates S. 1991. The crash of '87: Was it expected? The evidence from options markets. Journal of Finance 46:1009–44."]
  • ['———. 1996. Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Review of Financial Studies 9:69–107.']
  • ['Bodurtha, J., and G. Courtadon. 1987. Tests of an American option pricing model on the foreign exchange market. Journal of Financial and Quantitative Analysis 22:153–67.']
  • ['Campa, J., P. Chang, and R. Reider. 1998. Implied exchange rate distributions: Evidence from OTC option markets. Journal of International Money and Finance 17:117–60.']
  • ['Carr, P., H. Geman, D. Madan, and M. Yor. 2002. The fine structure of asset returns: An empirical investigation. Journal of Business 75:305–32.']
  • ['Carr, P., and L. Wu. 2001. What type of process underlies options? A simple robust test. Journal of Finance 58:2581–2610.']
  • ['Chang, K., and M. Kim. 2001. Jumps and time‐varying correlations in daily foreign exchange rates. Journal of International Money and Finance 20:611–37.']
  • ['Das, S. R., and R. K. Sundaram. 1999. Of smiles and smirks: A term structure perspective. Journal of Financial and Quantitative Analysis 34:211–39.']
  • ['Delbaen, F., P. Grandits, T. Rheinlönder, D. Samperi, M. Schweizer, and C. Stricker. 2002. Exponential hedging and entropic penalties. Mathematical Finance 12:99–123.']
  • ['Garman, M., and S. Kohlhagen. 1983. Foreign currency option values. Journal of International Money and Finance 2:231–37.']
  • ['Goll, T., and L. Rüschendorf. 2001. Minimax and minimal distance martingale measures and their relationship to portfolio minimization. Finance and Stochastics 5:557–81.']
  • ['Jorion, P. 1988. On jump processes in the foreign exchange and stock markets. Review of Financial Studies 1:427–45.']
  • ['Kabanov, Y., and C. Stricker. 2002. On the optimal portfolio for the exponential utility maximization: Remarks to the six‐author paper. Mathematical Finance 12:125–34.']
  • ['Madan, D., P. Carr, and E. Chang. 1998. The variance gamma process and option pricing. European Finance Review 2:79–105.']
  • ['Madan, D., and F. Milne. 1991. Option pricing with VG martingale component. Mathematical Finance 1:39–55.']
  • ['Madan, D., and E. Seneta. 1990. The variance gamma model for share market returns. Journal of Business 63:511–24.']
  • ['Merton, R. C. 1976. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3:125–44.']
  • ['Mizon, G., and J. Richard. 1986. The encompassing principle and its application to testing non‐nested hypotheses., Econometrica 54:657–68.']
  • ['Scott, L. 1997. Pricing stock options in a jump‐diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods. Mathematical Finance 7:413–26.']
  • ['Shastri, K., and K. Tandon. 1986. Valuation of foreign currency options: Some empirical tests. Journal of Financial and Quantitative Analysis 21:145–60.']