The analysis of diffusion process in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A methodology is proposed for estimating and testing coefficient functions for ergodic diffusions that are not directly observable. It is based on...

Despite many attempts, the consistent and global modelling of financial markets remains an open problem. In particular it remains a challenge to find a simple and tratable economic and probablistic approach to market modelling. This paper attempts to highlight fundamental properties that a...

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...

In the years following the publication of Black and Scholes [7], numerous alternative models have been proposed for pricing and hedging equity derivatives. Prominent examples include stochastic volatility models, jump diffusion models, and models based on Levy processes. These all have their own...

Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices,...

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. In the presence of jumps, maximizing the Sharpe...

We consider different approaches to the problem of numerically inverting Laplace transforms in finance. In particular, we discuss numerical inversion techniques in the context of Asian option pricing.

This paper considers a modification of the well-known constant elasticity of variance model where it is used to model the growth optimal portfolio. It is shown taht, for this application, there is no equivalent risk neutral pricing methodology fails. However, a consistent pricing and hedging...

This paper describes a two-factor model for a diversifed 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...

When simulating discrete time approximations of solutions of stochastic differential equations (SDEs), numerical stability is clearly more important than numerical efficiency or some higher order of convergence. Discrete time approximations of solutions of SDEs are widely used in simulations in...