Mixtures of t-distributions for Finance and Forecasting
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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- Yacine Aït-Sahalia & Andrew W. Lo, 1998.
"Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,"
Journal of Finance,
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- 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.
- 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.).
- Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
- Abadir, Karim, 1995. "An Introduction to Hypergeometric Functions for Economists," Discussion Papers 9510, Exeter University, Department of Economics.
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- 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. Full references (including those not matched with items on IDEAS)