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Inference for stochastic volatility models using time change transformations

Author

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  • Konstantinos Kalogeropoulos
  • Gareth O. Roberts
  • Petros Dellaportas

Abstract

We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic volatility. The methodology is tested through simulation based experiments and illustrated on data consisting of US treasury bill rates.

Suggested Citation

  • Konstantinos Kalogeropoulos & Gareth O. Roberts & Petros Dellaportas, 2007. "Inference for stochastic volatility models using time change transformations," Papers 0711.1594, arXiv.org.
  • Handle: RePEc:arx:papers:0711.1594
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    References listed on IDEAS

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    1. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
    3. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-338, July.
    4. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    5. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    6. Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382.
    7. Kalogeropoulos, Konstantinos, 2007. "Likelihood-based inference for a class of multivariate diffusions with unobserved paths," LSE Research Online Documents on Economics 31423, London School of Economics and Political Science, LSE Library.
    8. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Particle filters for partially observed diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 755-777.
    9. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    10. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    11. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    12. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    13. Konstantinos Kalogeropoulos & Petros Dellaportas & Gareth O. Roberts, 2007. "Likelihood-based inference for correlated diffusions," Papers 0711.1595, arXiv.org.
    14. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
    15. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
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    Citations

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    Cited by:

    1. Beskos, Alexandros & Kalogeropoulos, Konstantinos & Pazos, Erik, 2013. "Advanced MCMC methods for sampling on diffusion pathspace," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1415-1453.
    2. Konstantinos Kalogeropoulos & Petros Dellaportas & Gareth O. Roberts, 2007. "Likelihood-based inference for correlated diffusions," Papers 0711.1595, arXiv.org.
    3. Mario Cerrato & Chia Chun Lo & Konstantinos Skindilias, 2011. "Adaptive continuous time Markov chain approximation model to general jump-diffusions," Working Papers 2011_16, Business School - Economics, University of Glasgow.
    4. Giorgos Sermaidis & Omiros Papaspiliopoulos & Gareth O. Roberts & Alexandros Beskos & Paul Fearnhead, 2013. "Markov Chain Monte Carlo for Exact Inference for Diffusions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 294-321, June.
    5. Cerrato, Mario & Lo, Chia Chun & Skindilias, Konstantinos, 2011. "Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions," SIRE Discussion Papers 2011-53, Scottish Institute for Research in Economics (SIRE).

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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