Revista Ingenierías Universidad de Medellín
Print version ISSN 1692-3324
GRAJALES CORREA, Carlos Alexánder and PEREZ RAMIREZ, Fredy Ocaris. DISCRETE AND CONTINUOUS METHODS FOR MODELING FINANCIAL SERIES YIELDING STOCHASTIC VOLATILITY PROBABILITY DENSITY. Rev. ing. univ. Medellin [online]. 2007, vol.6, n.11, pp. 105-123. ISSN 1692-3324.
This work considers daily yields of financial assets in order to model and compare returns stochastic volatility probability density. For such aim, ARCH models and its extensions are proposed - they are in discrete time- as well as an Empirical Stochastic Volatility Model, developed by Paul Wilmott. For the discrete case, models that allow to estimate heteroscedasticity conditional volatility in a time, t, t,t∈[1,T], are shown. In the continuous case, there is an association of an Itô diffusion process to stochastic volatility of the financial series, which allows to write a discretization of this process and to simulate it to obtain empirical probabilistic densities from the volatility. Finally the results are illustrated and compared with methodologies exposed by the case of the financial series S&P 500 of the U.S.A., Index of Prices and Quotations of stock-market Mexican of Values (IPC) and IGBC of Colombia.
Keywords : Probability density function; ARCH; volatility; heteroscedasticity; Itô diffusion process; simulation.