Estimation of the parameters of stochastic differential equations

Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of the parameters of SDEs, however, a closed-form expression for the likelihood　function is rarely available and hence exact maximum-likelihood (EML) estimation is usually infeasible. The key research problem examined in this thesis is the development of generic, accurate and computationally feasible estimation procedures based on the　ML principle, that can be implemented in the absence of a closed-form expression for　the likelihood function. The overall recommendation to come out of the thesis is that　an estimation procedure based on the finite-element solution of a reformulation of the Fokker-Planck equation in terms of the transitional cumulative distribution function(CDF) provides the best balance across all of the desired characteristics. The recommended approach involves the use of an interpolation technique proposed in this thesis which greatly reduces the required computational effort.