Autori
Fornari, Fabio
Mele, Antonio

Titolo
Recovering the Probability Density Function of Asset Prices Using GARCH as Diffusion Approximations
Periodico
Banca d'Italia. Temi di discussione
Anno: 2001 - Volume: 2 - Fascicolo: 396 - Pagina iniziale: 1

This paper uses Garch models to estimate the objective and risk-neutral density functions of ¿nancial 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 ¿nance 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 pproximation 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 ¿tted to the historical path of the asset price. The risk-neutral PDF is extracted from cross-sections 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 VWDWHV RI QDWXUH. Applications are carried out with regard to the futures written on the Italian 10-year bond.



Testo completo: http://www.bancaditalia.it/pubblicazioni/temidi/td396/sintesi396.pdf

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