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Recovering the Probability Density Function of Asset Prices using Garch as Diffusion Approximations

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  • F. Fornari
  • A. Mele

Abstract

This paper uses Garch models to estimate the objective and risk-neutral density functions of financial asset prices and, by comparing their shapes, recover detailed information on economic agents' attitudes toward risk. It differs from recent papers investigating analogous issues because it uses Nelson's (1990) result that Garch schemes are approximations of the kind of differential equations typically employed in finance to describe the evolution of asset prices. This feature of Garch schemes usually has been overshadowed by their well-known role as simple econometric tools providing reliable estimates of unobserved conditional variances. We show instead that the diffusion approximation property of Garch gives good results and can be extended to situations with i) non-standard distributions for the innovations of a conditional mean equation of asset price changes and ii) volatility concepts different from the variance. The objective PDF of the asset price is recovered from the estimation of a nonlinear Garch fitted to the historical path of the asset price. The risk-neutral PDF is extracted from crosssections of bond option prices, after introducing a volatility risk premium function. The direct comparison of the shapes of the two PDFS reveals the price attached by economic agents to the different states of nature. Applications are carried out with regard to the futures written on the Italian 10-year bond.

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Bibliographic Info

Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2000-12.

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Date of creation: 2000
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Handle: RePEc:ema:worpap:2000-12

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  1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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  3. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
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Citations

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Cited by:
  1. Luca Dedola & Eugenio Gaiotti & Luca Silipo, 2001. "Money demand in the euro area: do national differences matter?," Temi di discussione (Economic working papers) 405, Bank of Italy, Economic Research and International Relations Area.
  2. Christian Conrad & Menelaos Karanasos & Ning Zeng, 2008. "Multivariate Fractionally Integrated APARCH Modeling of Stock Market Volatility: A multi-country study," Working Papers 0472, University of Heidelberg, Department of Economics, revised Jul 2008.
  3. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
  4. M. Karanasos & S. Schurer, 2006. "Is the relationship between ination and its uncertainty linear?," Computing in Economics and Finance 2006 463, Society for Computational Economics.
  5. Antonio Mele, 2002. "Fundamental Properties of Bond Prices in Models of the Short-Term Rate," Working Papers 460, Queen Mary, University of London, School of Economics and Finance.
  6. Fabio Fornari, 2002. "The size of the equity premium," Temi di discussione (Economic working papers) 447, Bank of Italy, Economic Research and International Relations Area.
  7. Fornari, Fabio, 2008. "Assessing the compensation for volatility risk implicit in interest rate derivatives," Working Paper Series 0859, European Central Bank.

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