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Inference for stochastic volatility model using time change transformations

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  • Kalogeropoulos, Konstantinos
  • Roberts, Gareth O.
  • Dellaportas, Petros

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5697.

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Date of creation: 2007
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Handle: RePEc:pra:mprapa:5697

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Keywords: Imputation; Markov chain Monte Carlo; Stochastic volatility;

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  1. 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.
  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. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  4. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-93, July.
  5. Kalogeropoulos, Konstantinos & Dellaportas, Petros & Roberts, Gareth O., 2007. "Likelihood-based inference for correlated diffusions," MPRA Paper 5696, University Library of Munich, Germany.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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 335-38, July.
  11. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
  12. 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 727-52.
  13. 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.
  14. 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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Cited by:
  1. Konstantinos Kalogeropoulos & Petros Dellaportas & Gareth O. Roberts, 2007. "Likelihood-based inference for correlated diffusions," Papers 0711.1595, arXiv.org.
  2. 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.

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