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Indirect estimation of alpha-stable stochastic volatility models

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Author Info
Marco Lombardi () (Universita' di Pisa. Diparimento di Matematica e Statistica per l'Economia)
Giorgio Calzolari () (Università degli Studi di Firenze, Dipartimento di Statistica "G. Parenti")

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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 diffusion among practitioners. In this paper we propose 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. We consider both cases of heavytailed noise in the returns or in the volatility. The approach is illustrated by means of a detailed simulation study and an application to currency crises.

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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica "G. Parenti" in its series Econometrics Working Papers Archive with number wp2006_07.

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Length: 24
Date of creation: Oct 2006
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Handle: RePEc:fir:econom:wp2006_07

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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. McCulloch, J. Huston, 1985. "Interest-risk sensitive deposit insurance premia : Stable ACH estimates," Journal of Banking & Finance, Elsevier, vol. 9(1), pages 137-156, March. [Downloadable!] (restricted)
  3. McCulloch, J Huston, 1978. "Continuous Time Processes with Stable Increments," Journal of Business, University of Chicago Press, vol. 51(4), pages 601-19, October. [Downloadable!] (restricted)
  4. 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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  5. 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)
  6. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October. [Downloadable!]
  7. 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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  8. 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)
  9. 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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  10. 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)
  11. 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)
  12. 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)
  13. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  14. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June. [Downloadable!] (restricted)
  15. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
  16. 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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  17. 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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  18. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  19. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1995. "Estimation of Stochastic Volatility Models with Diagnostics," Working Papers 95-36, Duke University, Department of Economics.
  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)
  21. J. Huston McCulloch, 2003. "The Risk-Neutral Measure and Option Pricing under Log-Stable Uncertainty," Working Papers 03-07, Ohio State University, Department of Economics. [Downloadable!]
  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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