A RATIONAL PROBABILITY DENSITY APPROACH TO STOCHASTIC VOLATILITY ESTIMATION

摘要

In the area of financial time series the Black-Scholes model is often used. However, it is well-known that although the volatility is assumed to be constant in the Black-Scholes model, in practice it is varying in time. This has led to the investigation of more general models in which the volatility is allowed to vary. In one class of such models the dynamic behavior of volatility is described by some stochastic process. A problem with such models is that it is generally very difficult to solve the volatility estimation problem for such models: the calculation of the conditional density of the volatility at some point in time, given the observations up till that point in time, is usually a difficult task for which there are no closed form expressions. In the present paper a class of models of the same type is presented, which however has the advantage that for these models the volatility estimation problem can be solved exactly. In our models all disturbances have a rational probability density function on the real line.