Short-courses and Tutorials

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

Class Day Date Time Room Topic
1st Monday Nov 23 16.30-18.00 N1-7 velodromo Normal dynamic linear models
2nd Tuesday Nov 24 10.30-12.00 SDA 01 via Bocconi Nonnormal, nonlinear dynamic models
3rd Tuesday Nov 24 16.30-18.00 N17 velodromo Stochastic volatility models
4th Wednesday Nov 25 10.30-12.00 4-C via Sarfatti More on SV models
5th Thursday Nov 26 10.30-12.00 4-1 via Sarfatti Sequential Monte Carlo methods
SEMINAR Nov 26 16.30-18.00 Particle Learning for General Mixtures (talk slides)
6th Friday Nov 27 10.30-11.50 N1-2 velodromo Particle learning (PL)
7th Friday Nov 27 12.10-13.30 N1-2 velodromo More on PL


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