Skip to main content

Non-linear Volatility Modeling in Classical and Bayesian Frameworks with Applications to Risk Management

  • Chapter
Adaptive Information Systems and Modelling in Economics and Management Science

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Blibliography

  • Alles, L. and Kling, J. (1994). Regularities in the variation of skewness in asset returns. Journal of Financial Research, 17:427–438.

    Google Scholar 

  • Bartlmae, K. and Rauscher, F. A. (2000). Measuring DAX market risk: A neural network volatility mixture approach. Presentation at the FFM2000 Conference, London, 31 May–2 June, can be downloaded from www.gloriamundi.org/picsresources.org/picsresources.

    Google Scholar 

  • Bauwens, L. and Lubrano, M. (1998). Bayesian inference on GARCH models usin Gibbs sampler. Econometrics Journa 1:23–46.

    Article  Google Scholar 

  • Bishop, C. (1994). Mixture density networks. Technical report, Neural Computing Research Group Report: NCRG/94/004, Aston University, Birmingham.

    Google Scholar 

  • Bishop, C. (1995). Neural Networks for Pattern Recognition. Clarendon Press, Oxford.

    Google Scholar 

  • Boero, G. and Cavallil, E. (1997). Exchange rate forecasting: Neural networks versus linear econometric models. Neural Network World, 1:29–42.

    Google Scholar 

  • Bollerslev, T. (1986). A generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31:307–327.

    Article  Google Scholar 

  • Brooks, S. (1998). Markov chain Monte Carlo method and its application. The Statisician, 47:69–100.

    Google Scholar 

  • Carlin, B. and Louis, T. (1996). Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall, London.

    Google Scholar 

  • Chib, S. and Greenberg, E. (1996). Markov Chain Monte Carlo simulation methods in econometrics. Econometric Theory, 12:409–431.

    Google Scholar 

  • Chib, S. and Jeliazhov, I. (2001). Marginal likelihood from the Metropolis-Hastings output. Journal od American Stattistical Association, 96(453):270–281.

    Article  Google Scholar 

  • Diebolt, J. and Robert, C. (1994). Estimation of finite mixture distributions through bayesian sampling. Journal of the Royal Statistical Society, series B, 56:363–375.

    Google Scholar 

  • Dowd, K. (1998). Beyond Value at Risk: the New Science of Risk Management. John Willey & Sons, London.

    Google Scholar 

  • Duffie, D. and Pan, J. (1997). An overview of value at risk. Journal of Derivatives, 4:7–49.

    Google Scholar 

  • Dunis, C. L. and Jalilov, J. (2002). Neural network regression and alternative forecasting techniques for predicting financial variables. Neural Network World, 12:113–139.

    Google Scholar 

  • Frühwirth-Schnatter, S. (2001). MCMC estimation of classical and dynamic switching and mixture models. Journal of the American Statistical Association, 96:194–209.

    Article  Google Scholar 

  • Geman, S., Bienenstock, E., and Doursat, R. (1992). Neural networks and the bias/variance dilemma. Neural Computation, 4:1–58.

    Google Scholar 

  • Geweke, J. (1993). Bayesian treatment of the independent student-t linear model. Journal of Applied Econometrics, 8:19–40.

    Article  Google Scholar 

  • Geweke, J. (1995). Bayesian comparison of econometric models. Working Papers 532, Federal Reserve Bank of Minneapolis.

    Google Scholar 

  • Geweke, J. (1999). Using simulation methods for bayesian econometric models: Inference, development and communication. Econometric Reviews, 18:1–126.

    Article  Google Scholar 

  • Gilks, W., Richardson, S., and Spiegelhalter, D. (1996). Markov Chain Monte Carlo in Practice. Chapman & Hall, London.

    Google Scholar 

  • Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48:1779–1801.

    Article  Google Scholar 

  • González, M. and Burgess, N. (1997). Modelling market volatilities: the neural network perspective. The European Journal of Finance, 3:137–157.

    Article  Google Scholar 

  • Green, P. (1995). Reversible jump MCMC computation and Bayesian model determination. Biometrika, 82:711–732.

    Article  Google Scholar 

  • Hansen, B. (1994). Autoregressive conditional density estimation. International Economic Review, 35:705–730.

    Article  Google Scholar 

  • Holmes, C. and Mallick, B. (1998). Bayesian radial basis functions of variable dimension. Neural Computation, 10:1217–1233.

    Article  Google Scholar 

  • Hornik, K., Stinchcombe, M., and White, H. (1989). Multilayer feedforward networks are universal approximators. Neural Networks, 2:359–366.

    Article  Google Scholar 

  • Jeffreys, H. (1961). Theory of Probability, 3rd edition. Oxford Univiersity Press, Oxford.

    Google Scholar 

  • Kass, R. and Raftery, A. (1995). Bayes factor. Journal od American Statistical Association, 90:773–792.

    Article  Google Scholar 

  • Kaufmann, S. and Frühwirth-Schnatter, S. (2002). Bayesian analysis of switching ARCH models. Journal of Time Series Analysis, 23(4):425–458.

    Article  Google Scholar 

  • Kim, S., Shephard, N., and Chib, S. (1998). Stochastic volatility: Likelihood inference and comparison with ARCH models. Review of Economic Studies, 65:361–393.

    Article  Google Scholar 

  • Kleibergen, F. and van Dijk, H. (1993). Non-stationarity in GARCH models: a bayesian analysis. Journal of Applied Econometrics, 8:41–61.

    Article  Google Scholar 

  • Kupiec, H. (1995). Techniques for verifying the accuracy of risk management models. Journal of Derivatives, 3:73–84.

    Google Scholar 

  • MacKay, D. (1992). A practical bayesian framework for backprop networks. Neural Computation, 4:448–472.

    Article  Google Scholar 

  • Marrs, A. (1998). An application of reversible-jump MCMC to multivariate spherical gaussian mixtures. In Jordan, M., Kearns, M., and Solla, S., editors, Advances in Neural Information Processing Systems, volume 10, pages 577–583. MIT Press, Cambridge, Mass.

    Google Scholar 

  • Meng, X. and Wong, W. (1996). Simulating ratios of normalizing constants via a simple identity. Statistical Sinica, 6:831–860.

    Google Scholar 

  • Miazhynskaia, T., Dockner, E. J., and Dorffner, G. (2003a). On the economic costs of value at risk forecast. Technical report, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna. Submitted to Journal of Banking and Finance, can be downloaded from http://www.wu-wien.ac.at/am/reports.htm.

    Google Scholar 

  • Miazhynskaia, T., Dorffner, G., and Dockner, E. J. (2003b). Non-linear versus non-gaussian volatility models in application to different financial markets. Technical report, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna. Can be downloaded from http://www.wu-wien.ac.at/am/reports.htm.

    Google Scholar 

  • Miazhynskaia, T., Frühwirth-Schnatter, S., and Dorffner, G. (2003c). A comparison of bayesian model selection based on mcmc with an application to garch-type models. Technical report, SFB Adaptive Information Systems and Modelling in Economics and Management Science. Can be downloaded from http://www.wu-wien.ac.at/am/reports.htm.

    Google Scholar 

  • Müller, P. and Insua, D. R. (1998). Issues in bayesian analysis of neural network models. Neural Computation, 10:571–592.

    Article  Google Scholar 

  • Müller, P. and Pole, A. (1998). Monte carlo posterior integration in GARCH models. Sankhya-The Indian Journal of Statistics, 60:127–144.

    Google Scholar 

  • Nakatsuma, T. (2000). Bayesian analysis of ARMA-GARCH models: a Markov chain sampling approach. Journal of Econometrics, 95:57–69.

    Article  Google Scholar 

  • Neal, R. (1996). Bayesian Learning for Neural Networks. Springer, New York.

    Google Scholar 

  • Nelson, D. (1991). Conditional heteroskedasticity in asset returns: a new approach. Econometrica, 59:347–370.

    Article  Google Scholar 

  • Poh, H.-L., Yao, J. T., and Jasic, T. (1998). Neural networks for the analysis and fore-casting of advertising and promotion impact. International Journal of Intelligent Systems in Accounting, Finance and Management, 7(4):253–268.

    Article  Google Scholar 

  • Prechelt, L. (1998). Early stopping-but when? In Orr, G. and Müller, K.-R., editors, Neural Networks: Tricks of the Trade, pages 55–69. Springer, Berlin.

    Chapter  Google Scholar 

  • Reed, R. (1993). Prunung algorithm-a survey. IEEE Transactions on Neural Networks, 4(5):740–746.

    Article  Google Scholar 

  • Richardson, S. and Green, P. (1997). On Bayesian analysis of mixtures with an unknown number of components. Journal of the Royal Statistical Society, Series B, 59:731–792.

    Article  Google Scholar 

  • Robert, C. (1996). Mixtures of distributions: Inference and estimation. In Gilks, W., Richardson, S., and Spiegelhalter, D., editors, Markov Chain Monte Carlo in Practicd, pages 441–464. Chapman & Hall.

    Google Scholar 

  • Schittenkopf, C., Dorffner, G., and Dockner, E. J. (1999). Non-linear versus non-gaussian volatility models. Technical report, SFB Adaptive Information Systems and Modelling in Economics and Management Science, Vienna.

    Google Scholar 

  • Schittenkopf, C., Dorffner, G., and Dockner, E. J. (2000). Forecasting time-dependent conditional densities: a seminonparametric neural network approach. Journal of Forecasting, 19:355–374.

    Article  Google Scholar 

  • Stephens, M. (1997). Bayesian methods for mixture of normal distributions. Technical report, Department of Statistics, Oxford University, England.

    Google Scholar 

  • Swanson, N. and Franses, P. (1999). Nonlinear econometric modelling: a selective review. In Rothman, P., editor, Nonlinear Timee Series Analysis of Economic and Financial Data, pages 87–110. Kluwer Academic, Dordrecht.

    Google Scholar 

  • Tierney, L. (1994). Markov chains for exploring posterior distributions. Annals of Statistics, 21:1701–1762.

    Article  Google Scholar 

  • Vrontos, I., Dellaportas, P., and Politis, D. (2000). Full Bayesian inference for GARCH and EGARCH models. Journal of Business & Economic Statistics, 18(2):187–198.

    Article  Google Scholar 

  • Yao, J. T., Tan, C. L., and Li, Y. L. (2000). Option prices forecasting using neural networks. International Journal of Management Science, 28(4):455–466.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag/Wien

About this chapter

Cite this chapter

Miazhynskaia, T., Dockner, E., Frühwirth-Schnatter, S., Dorffner, G. (2005). Non-linear Volatility Modeling in Classical and Bayesian Frameworks with Applications to Risk Management. In: Taudes, A. (eds) Adaptive Information Systems and Modelling in Economics and Management Science. Interdisciplinary Studies in Economics and Management, vol 5. Springer, Vienna. https://doi.org/10.1007/3-211-29901-7_5

Download citation

  • DOI: https://doi.org/10.1007/3-211-29901-7_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-20684-3

  • Online ISBN: 978-3-211-29901-2

  • eBook Packages: Business and Economics

Publish with us

Policies and ethics