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Mixtures of t-distributions for Finance and Forecasting

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  • Giacomini, Raffaella

    (University College London)

  • Gottschling, Andreas

    (Deutsche Bank AG, Credit RiskManagement)

  • Haefke, Christian

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

  • White, Halbert

    (Department of Economics, University of California, San Diego)

Abstract

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. A feature that makes this family particularly desirable for econometric applications is that it possesses closed-form expressions for its anti-derivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we use a scaled and shifted t-distribution to produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-of-sample, than density forecasts obtained using normal or standard t-distributions. In the second application, we replicate the option-pricing exercise of Abadir and Rockinger (2003) using a mixture of scaled and shifted t-distributions and obtain comparably good results, while gaining analytical tractability.

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File URL: http://www.ihs.ac.at/publications/eco/es-216.pdf
File Function: First version, 2007
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Bibliographic Info

Paper provided by Institute for Advanced Studies in its series Economics Series with number 216.

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Length: 27 pages
Date of creation: Oct 2007
Date of revision:
Handle: RePEc:ihs:ihsesp:216

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Related research

Keywords: ARMA-GARCH models; neural networks; nonparametric density estimation; forecast accuracy; option pricing; risk neutral density;

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  1. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  2. Abadir, Karim M. & Rockinger, Michael, 2003. "Density Functionals, With An Option-Pricing Application," Econometric Theory, Cambridge University Press, vol. 19(05), pages 778-811, October.
  3. Abadir, Karim, 1995. "An Introduction to Hypergeometric Functions for Economists," Discussion Papers 9510, Exeter University, Department of Economics.
  4. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  5. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  6. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  7. Yi-Ting Chen & Chung-Ming Kuan, 2002. "Time irreversibility and EGARCH effects in US stock index returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 565-578.
  8. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(01), pages 91-115, March.
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Cited by:
  1. Juan Carlos Martínez-Ovando & Stephen G. Walker, 2011. "Time-series Modelling, Stationarity and Bayesian Nonparametric Methods," Working Papers 2011-08, Banco de México.
  2. Chang, Kuang-Liang, 2012. "Volatility regimes, asymmetric basis effects and forecasting performance: An empirical investigation of the WTI crude oil futures market," Energy Economics, Elsevier, vol. 34(1), pages 294-306.
  3. Wolfgang Karl Härdle & Brenda López-Cabrera & Huei-Wen Teng, 2013. "State Price Densities implied from weather derivatives," SFB 649 Discussion Papers SFB649DP2013-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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