Many common option pricing problems require numerical solution techniques. One standard tool is to solve a finite difference approximation to the instrument's fundamental partial differential equation (PDE), with appropriate boundary conditions. The approximation will converge to the true...

Two maximum likelihood methods for estimating the parameters of stochastic differential equations (SDEs) from time-series data are proposed. The first is that of simulated maximum likelihood in which a nonparametric kernel is used to construct the transitional density of an SDE from a series of...

A quasi-maximum likelihood procedure for estimating the parameters of multi-dimensional diffusions is developed in which the transitional density is a multivariate Gaussian density with first and second moments approximating the true moments of the unknown density. For affine drift and diffusion...

In many electricity markets, retailers purchase electricity at an unregulated spot price and sell to consumers at a heavily regulated price. Consequently, the occurrence of spikes in the spot electricity price represents a major source of risk for retailers, and the forecasting of these price...

In many electricity markets, retailers purchase electricity at an unregulated spot price and sell to consumers at a heavily-regulated price. Consequently the occurrence of extreme movements in the spot price represent a major source of risk to retailers and the accurate forecasting of these...

Time series data consisting of 671 observations of seawater temperature, observed at irregular intervals off Maria Island, Hobart, Australia, over a period of 50 years, are examined. The mean temperature exhibits an approximately linear trend which is taken as evidence of glabal warming.