Simulation and statistical methods for stochastic differental equations

Abstract

We look at numerical methods for simulation of stochastic differential equations exhibiting volatility induced stationarity. This is a property of the process which means that the stationary behaviour is mostly imposed by how volatile the process is. The property creates issues in simulation and hence also in statistical methods. The methods considered for simulations are the fully implicit Euler scheme and timechanged simulation. We look at statistical methods for estimation of parameters. The specific statistical methods we investigate is the likelihood ratio, which gives expressions for the drift parameters for CKLS and least squares estimation, which is used together with quadratic variation to estimate parameters in different models.