Phénomènes financiers et mélange de lois : Une nouvelle méthode d’estimation des paramètres.

Chilarescu, Constantin and Viasu, Ioana Luciana (2011): Phénomènes financiers et mélange de lois : Une nouvelle méthode d’estimation des paramètres.

Abstract

The main aim of this paper is to examine the qualities of the mixed diffusion-jump process whose parameters are random variables. The hypothesis of a Wiener geometric process applied to exchange rate has become doubtful at the beginning of the nineties, fact determined by a high leptokurtosis of the empirical distributions. The alternative of another distribution was studied in several articles. The mathematical model proposed in this paper has as fundamental hypothesis the fact that the distribution of the continuous part of the changes in the logarithms of exchange rate is a mixture of normals whose parameters are random variables.

• Item Type: MPRA Paper
• Language: French
• Keywords: mixed diffusion-jump process; mixture of normals
• Subjects: C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling

References

1. K. K. Aase and P. Guttorp: Estimation in Models for Security Prices. Scandinavian Actuarial Journal, (1987), 213 – 223.

2. V. Akgiray and G. G. Booth: Mixed Diffusion – Jump Process Modeling of Exchange Rate Movements. Review of Economics and Statistics, (1988), 631 – 637.

3. C. Ball and W. N. Torus: On Jumps in Common Stock Prices and Their Impact on Call Option Pricing. Journal of Finance, 1 (1985), 155 – 173.

4. D. S. Bates: Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Option. Review of Financial Studies, 1 (1996), 69 – 107.

5. P. Boothe and D. Glassman: The Statistical Distribution of Exchange Rates. Empirical Evidence and Economic Implications. Journal of International Economics, 22 (1987), 297 – 319.

6. C. Chilarescu: Modélisation du comportement et du risque des actifs financiers roumains et des facteurs explicatifs. Edition de l’Université de Timisoara, 1996.

7. I. Domowitz and C . S. Hakkio: Conditional Variance and the Risk Premium in the Foreign Exchange Market. Journal of International Economics, 19 (1985) 47 – 66.

8. S. Herzel: A Simple Model for Option Pricing with Jumping Stochastic Volatility. International Journal of Theoretical and Applied Finance, 4 (1998), 487 – 505.

9. D. A. Hsieh: The Statistical Properties of Daily Foreign Exchange Rates : 1974 – 1983. Journal of International Economics, 24 (1988), 129 – 145.

10. N. Ikeda and S. Watanabe: Stochastic Differential Equations and Diffusion Processes. North – Holland, 1981.

11. R. Jarrow and E. Rosenfeld: Jump Risk and the Intertemporal Capital Asset Pricing Model. Journal of Business. 57 (1984), 337 – 351.

12. Ph. Jorion: On Jump Processes in the Foreign Exchange and Stock Markets. Review of Financial Studies, 4 (1988), 427 – 445.

13. I. Karatzas and S. E. Shreve: Brownian Motion and Stochastic Calculus. Springer Verlag, 1988.

14. M. J. Kim, Y. H. Oh and R. Brooks: Are Jumps in Stock Return Diversifiable ? Evidence and Implication for Option Pricing. Journal of Financial and Quantitative Analysis, (1994), 609 – 631.

15. R. E. Quandt and J. B. Ramsey: Estimating Mixtures of Normal Distributions and Switching Regressions. Journal of the American Statistical Association, 364 (1978), 730 – 752.

16. A. L. Tucker and L. Pond: The Probability Distribution of Foreign Exchange Price Changes : Tests of Candidate Processes. Review of Economics and Statistics, (1988), 638 – 647.

17. H. von Weizsacker and G. Winkler: Stochastic Integral. Vieweg Advanced Lectures in Mathematics, 1990.

18. N. Zamfirescu et C . Chilarescu: Estimation des paramètres d’un mélange de lois normales provenant d’un modèle saut – diffusion à volatilité stochastique à deux états. Journal de la Société Statistique de Paris, 2 (1998).