This paper derives a unified framework for portfolio optimization, derivative pricing, financial modeling and risk measurement. It is based on the natural assumption that investors prefer more or less, in the sense that the higher drift is preferred. Each such investor is shown to hold an...

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...

The paper describes a continuous time share market model with a minimal number of factors. These factors are powers of Bessel processes. The asset prices are formed by ratios of the factors and have consequently leptokurtic return distributions. In this framework stochastic volatility with...

The paper proposes a financial market model that generates stochastic volatilities and stochastic interest rates using a minimal number of factors that characterise the dynamics of different denominations of a benchmark portfolio. It models asset prices essentially as functionals of square root...

Starting from the European option valuation framework of Chauveau and Gatfaoui (2002), we establish the link with stochastic volatility models. And, we propose both a new vision and a general framework for valuing European options in the light of systematic and idiosyncratic risks affecting...

This paper builds upon the authors' previous work on transformation of the Heath-Jarrow-Morton (HJM) model of the term structure of interest rates to state space form for a fairly general class of volatility specification including stochastic variables. Estimation of this volatility function is...

The paper considers the continuous time pricing and hedging of European options in the presence of small transaction costs and frequent trading under local risk minimisation. The approach yields mean-self-financing strategies. The resulting dynamical hedges adapt the trading frequency in...

We investigate the existence of affine realizations for interest rate term structure models driven by Levy processes. Using as numeraire the growth optimal portfolio, we model the interest rate term structure under the real-world probability measure, and hence, we do not need the existence of an...

This paper proposes a framework for pricing credit derivatives within the defaultable Markovian HJM framework featuring unspanned stochastic volatility. Motivated by empirical evidence, hump-shaped level dependent stochastic volatility specifications are proposed, such that the model admits...

In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method...