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Modeling heteroscedastic, skewed and leptokurtic returns in discrete time

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  • Ivivi Joseph Mwaniki

Abstract

Popular models of finance, fall short of accounting for most empirically found stylized features of financial time series data, such as volatility clustering, skewness and leptokurtic nature of log returns. In this study we propose a general framework for modeling asset returns which account for serial dependencies in higher moments and leptokurtic nature of scaled GARCH filtered residuals. Such residuals are calibrated to normal inverse Gaussian and hyperbolic distribution. Dynamics of risky assets assumed in Black Scholes model, Duans GARCH model and other benchmark models for contract valuation, are shown to be nested in the the proposed framework.Keywords: Stylized facts; Normal inverse Gaussian; GARCH model; Hyperbolic distribution; leptokurtic returns

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  • Ivivi Joseph Mwaniki, 2019. "Modeling heteroscedastic, skewed and leptokurtic returns in discrete time," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 9(5), pages 1-1.
    • Handle: RePEc:spt:apfiba:v:9:y:2019:i:5:f:9_5_1
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    1. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    2. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    5. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 755-793, April.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Tina Hviid Rydberg, 2000. "Realistic Statistical Modelling of Financial Data," International Statistical Review, International Statistical Institute, vol. 68(3), pages 233-258, December.
    8. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    9. 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.
    10. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    11. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    12. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
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