| The stochastic modeling of financial assets is essential to the valuation of financial products and investment decisions. These models are governed by certain parameters that are estimated through a process known as calibration. Current procedures typically perform a grid-search optimization of a given objective function over a specified parameter space. These methods can be computationally intensive and require restrictions on the parameter space to achieve timely convergence. In this thesis, we propose an alternative Kalman Smoother Expectation Maximization procedure (KSEM) that can jointly estimate all the parameters and produces better model fit that compared to alternative estimation procedures. Further, we consider the additional complexity of the modeling of jumps or spikes that may occur in a time series. For this calibration we develop a Particle Smoother Expectation Maximization procedure (PSEM) for the optimization of nonlinear systems. This is an entirely new estimation approach, and we provide several examples of its application. |
