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...

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...

This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is...

This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market...

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...

An algorithm is proposed for the discrete approximation of continuous market price processes that uses trees instead of lattices. It is shown that it is convergent when used for pricing both European and American options and that it is more efficient, for some models, than the usual recombining...

This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes as given an initial forward rate curve and a family of potential stochastic processes for its...