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Modelling the Stochastic Dynamics of Volatility for Equity Indices

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Abstract

The paper is based on the observations that stockk index returns of major equity markets are likely to be Student t distributed. It then develops a class of continuous time stochastic volatility models that is consistent with such empirical findings. Furthermore, applying the criterion of local risk minimisation in an incomplete market setting, option prices are computed. Finally it is shown that implied volatility smile and skew patterns of the type observed in the markets can be recovered from the resulting stochastic volatility model.

Suggested Citation

  • David Heath & Simon Hurst & Eckhard Platen, 1999. "Modelling the Stochastic Dynamics of Volatility for Equity Indices," Research Paper Series 7, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:7
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992. "Option Pricing Under Incompleteness and Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 2(3), pages 153-187, July.
    3. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413, October.
    4. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 143-151, June.
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    6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    7. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    8. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
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    12. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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    15. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    16. Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 4(2), pages 97-124, May.
    17. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    18. Eckhard Platen, 1999. "On the Log-Return Distribution of Index Benchmarked Share Prices," Research Paper Series 22, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    20. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
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    Cited by:

    1. David Heath & Eckhard Platen, 2004. "Understanding the Implied Volatility Surface for Options on a Diversified Index," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 55-77, March.
    2. Leah Kelly, 2004. "Inference and Intraday Analysis of Diversified World Stock Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2004, January-A.

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