Author(s)

C. Skaug

Abstract

When we use stochastic differential equations as models of financial data that appear as time series, we have to estimate the equation parameters. For complex models this is not straightforward. Approximate maximum likelihood methods are useful tools for this purpose. We suggest the following approach: The likelihood function given by the time series and the parameters is estimated for fixed values of the parameter vector. We apply a standard optimization method that repeatedly calls the estimation procedure, with different parameter vectors as arguments, until the optimization converges. The likelihood function is the product of the transition probability densities given by the data. By solving the Fokker-Planck equation associated with the stochastic differential equation, one can obtain these probability densities. Exact, analytical solut

Keywords