We present and evaluate a numerical optimization method (together with an algorithm for choosing the starting values) pertinent to the constrained optimization problem arising in the estimation of the GARCH models with inequality constraints, in particular the Simplified Component GARCH Model...

As hedge fund replication based on factor models has encountered growing interest among professionals and academics, and despite the launch of numerous products (indexes and mutual funds) in the past year, it faced many critics. In this paper, we consider three of the main critiques, namely the...

In this paper, we present algorithms to solve a complex system of partial integro-differential equations (PIDE's) of parabolic type. The system is motivated by applications in finance where the solution of the system gives the price of European options in a regime-switching jump diffusion model....

We explore the relation between correlation dimension, approximate entropy and sample entropy parameters, which are commonly used in nonlinear systems analysis. Using theoretical considerations we identify the points which are shared by all these complexity algorithms and show explicitly that...

Numerical solutions of SDDE often reflect to only a limited extent the exact solution behaviour. Hence it is necessary to identify those parameters of SDDE and algorithm for which a numerical method in use is reliable. For affine SDDE test equations, there exist estimates of the stability...

Numerical solutions of SDDE often reflect to only a limited extent the exact solution behaviour. Hence it is necessary to identify those parameters of SDDE and algorithm for which a numerical method in use is reliable. For affine SDDE test equations, there exist estimates of the stability...