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Time-independent models of asset returns revisited

Author

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  • Gillemot, L.
  • Töyli, J.
  • Kertesz, J.
  • Kaski, K.

Abstract

In this study we investigate various well-known time-independent models of asset returns being simple normal distribution, Student t-distribution, Lévy, truncated Lévy, general stable distribution, mixed diffusion jump, and compound normal distribution. For this we use Standard and Poor's 500 index data of the New York Stock Exchange, Helsinki Stock Exchange index data describing a small volatile market, and artificial data. The results indicate that all models, excluding the simple normal distribution, are, at least, quite reasonable descriptions of the data. Furthermore, the use of differences instead of logarithmic returns tends to make the data looking visually more Lévy-type distributed than it is. This phenomenon is especially evident in the artificial data that has been generated by an inflated random walk process.

Suggested Citation

  • Gillemot, L. & Töyli, J. & Kertesz, J. & Kaski, K., 2000. "Time-independent models of asset returns revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 304-324.
    • Handle: RePEc:eee:phsmap:v:282:y:2000:i:1:p:304-324
    DOI: 10.1016/S0378-4371(00)00101-1
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    1. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Vedat Akgiray & G. Geoffrey Booth, 1987. "Compound Distribution Models Of Stock Returns: An Empirical Comparison," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(3), pages 269-280, September.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    4. M. F. M. Osborne, 1959. "Brownian Motion in the Stock Market," Operations Research, INFORMS, vol. 7(2), pages 145-173, April.
    5. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    6. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    7. Fama, Eugene F, 1970. "Multiperiod Consumption-Investment Decisions," American Economic Review, American Economic Association, vol. 60(1), pages 163-174, March.
    8. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    9. Tucker, Alan L, 1992. "A Reexamination of Finite- and Infinite-Variance Distributions as Models of Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 73-81, January.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    11. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    12. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    13. Hagerman, Robert L, 1978. "More Evidence on the Distribution of Security Returns," Journal of Finance, American Finance Association, vol. 33(4), pages 1213-1221, September.
    14. Perry, Philip R., 1983. "More Evidence on the Nature of the Distribution of Security Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(2), pages 211-221, June.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    16. Kullmann, L & Töyli, J & Kertesz, J & Kanto, A & Kaski, K, 1999. "Characteristic times in stock market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 98-110.
    17. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
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