This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event-driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the...

This paper describes a two-factor model for a diversified market index using the growth optimal portfolio with a stochastic and possibly correlated intrinsic timescale. The index is modelled using a time transformed squared Bessel process with a log-normal scaling factor for the time...

Standard Monte Carlo methods can often be significantly improved with the addition of appropriate variance reduction techniques. In this paper a new and powerful variance reduction technique is presented. The method is based directly on the Ito calculus and is used to find unbiased...

When simulating discrete-time approximations of solutions of stochastic differential equations (SDEs), in particular martingales, numerical stability is clearly more important than some higher order of convergence. Discrete-time approximations of solutions of SDEs with multiplicative noise,...

This paper considers a modification of the well known constant elasticity of variance model where it is used to model the growth optimal portfolio (GOP). It is shown that, for this application, there is no equivalent risk neutral pricing measure and therefore the classical risk neutral pricing...

The analysis of diffusion processes in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A new model for a stock market index process is proposed in which the index is decomposed into an average growth process and an ergodic diffusion. The...

Without requiring the existence of an equivalent risk-neutral probability measure this paper studies a class of one-factor local volatility function models for stock indices under a benchmark approach. It is assumed that the dynamics for a large diversified index approximates that of the growth...