Monte Carlo Methods and Stochastic Volatility

Dipartimento di Scienze delle Decisioni
Universita Bocconi, Milano
November 23rd to 27th 2009

Course material: PDF FILE WITH 224 SLIDES

Course schedule

R code

• Dynamic linear models: dlm.R – lineargrowthmodel.R – dlm-ffbs.R
• Non-linear dynamic model: nonlineardynamicmodel.R
• Stochastic volatility model: sv-ar1.R
• SISR filter: dlm-smc.R – bootstrapfilter-stepbystep.R – bootstrapfilter-inclassBocconi.R
• Particle smoother: dlm-smc-smoothing.R
• LW filter: dlm-smc-learningsig2-LW.R – nonlinearmodel-LW.R – sv-LW.R
• PL: dlm-smc-learningsig2-PL.R
• LW, LWFA, APFSS an PL: lw-lwfa-apfss-pl.R

Basic references

• 1. Carlin, Polson and Stoffer (1992) A Monte Carlo approach to nonnormal and nonlinear state space modeling.
  Journal of the American Statistical Association, 87, 493-500.
• 2. Carvalho, Johannes, Lopes and Polson (2008) Particle Learning and Smoothing.
  Technical Report. The University of Chicago Booth School of Business.
• 3. Eraker, Johannes and Polson (2003) The Impact of Jumps in Volatility and Returns.
  Journal of Finance, 58, 1269-1300.
• 4. Gamerman and Lopes (2006) MCMC: Stochastic Simulation for Bayesian Inference.
  Baton Rouge: Chapman & Hall/CRC.
• 5. Jacquier, Polson and Rossi (1994) Bayesian Analysis of Stochastic Volatility Models.
  Journal of Business and Economic Statistics, 12, 371-89.
• 6. Johannes and Polson (2009) MCMC methods for Financial Econometrics.
  In Handbook of Financial Econometrics (Eds Y. Ait-Sahalia and L. Hansen). Oxford: Elsevier, 1-72.
• 7. Johannes, Polson and Stroud (2009) Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices.
  Review of Financial Studies, 22, 2559-2599.
• 8. Kim, Shephard and Chib (1994) Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models.
  Review of Economic Studies, 65, 361-393.
• 9. Liu and West (2001) Combined parameters and state estimation in simulation-based filtering.
  In Sequential Monte Carlo Methods in Practice (Eds. A. Doucet, N. de Freitas and N. Gordon).
  New York: Springer-Verlag, 197-223.
• 10. Gordon, Salmond and Smith (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation.
  Radar and Signal Processing, IEE Proceedings F 140, 107-113.
• 11. Migon, Gamerman, Lopes and Ferreira (2005) Dynamic models.
  In Handbook of Statistics, Volume 25: Bayesian Thinking, Modeling and Computation (Eds. D. Dey and C. R. Rao),
  Amsterdam: Elsevier, 553-588.
• 12. Petris, Petrone and Campagnoli (2009) Dynamic Linear Models with R.
  New York: Springer.
• 13. Pitt and Shephard (1999) Filtering via simulation: auxiliary particle filters.
  Journal of the American Statistical Association, 94, 590-599.
• 14. Polson, Lopes and Carvalho (2009) Bayesian Statistics with a Smile: a Resampling-Sampling Perspective.
  Technical Report. The University of Chicago Booth School of Business.
• 15. Polson, Stroud and Muller (2008) Practical Filtering with Sequential Parameter Learning.
  Journal of the Royal Statistical Society, Series B, 70, 413-428.
• 16. Prado and West (2010) Time Series: Modelling, Computation and Inference.
  Baton Rouge: Chapman & Hall/CRC.
• 17. Storvik (2002) Particle filters in state space models with the presence of unknown static parameters.
  IEEE Transactions of Signal Processing, 50, 281-289.
• 18. West and Harrison (1997) Bayesian Forecasting and Dynamic Models (2nd edition).
  New York: Springer-Verlag.

Other useful links

• International Society for Bayesian Analysis (ISBA)
• The R project
• Sequential Monte Carlo homepage