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Indirect estimation of [alpha]-stable stochastic volatility models

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Author Info
Lombardi, Marco J.
Calzolari, Giorgio

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Abstract

The [alpha]-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its many useful properties, including a central limit theorem, are especially appreciated in the financial field. However, estimation difficulties have up to now hindered its widespread use among practitioners. The authors introduce an indirect estimation approach to stochastic volatility models with [alpha]-stable innovations that exploits, as auxiliary model, a GARCH(1, 1) with t-distributed innovations. The approach is illustrated by means of a detailed simulation study and an application to currency crises.

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Publisher Info
Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 53 (2009)
Issue (Month): 6 (April)
Pages: 2298-2308
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Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2298-2308

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  1. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September. [Downloadable!] (restricted)
  2. Ghose, Devajyoti & Kroner, Kenneth F., 1995. "The relationship between GARCH and symmetric stable processes: Finding the source of fat tails in financial data," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 225-251, September. [Downloadable!] (restricted)
  3. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May. [Downloadable!] (restricted)
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  8. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  9. Philipp Hartmann & Stefan Straetmans & Caspar G. de Vries, 2004. "Fundamentals and joint currency crises," Working Paper Series 324, European Central Bank. [Downloadable!]
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  10. Marco J. Lombardi & Giorgio Calzolari, 2004. "Indirect estimation of alpha-stable distributions and processes," Econometrics Working Papers Archive wp2004_07, Universita' degli Studi di Firenze, Dipartimento di Statistica "G. Parenti". [Downloadable!]
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  11. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, 04. [Downloadable!] (restricted)
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  12. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Blackwell Publishing, vol. 71(4), pages 945-973, October. [Downloadable!] (restricted)
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  14. Lombardi, Marco J., 2007. "Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2688-2700, February. [Downloadable!] (restricted)
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  15. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06. [Downloadable!] (restricted)
  16. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  17. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De. [Downloadable!] (restricted)
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  18. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1995. "Estimation of Stochastic Volatility Models with Diagnostics," Working Papers 95-36, Duke University, Department of Economics.
  19. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-85, July-Sept. [Downloadable!] (restricted)
  20. Knut Heggland & Arnoldo Frigessi, 2004. "Estimating functions in indirect inference," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 447-462. [Downloadable!] (restricted)
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  22. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA. [Downloadable!]
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  23. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November. [Downloadable!] (restricted)
  24. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
    Other versions:
  25. Alvaro Cartea & Sam Howison, 2004. "Option Pricing with Levy-Stable Processes," OFRC Working Papers Series 2004mf01, Oxford Financial Research Centre. [Downloadable!]
  26. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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