Financial models are largely used in option pricing. These physical models capture several salient features of asset price dynamics. The pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches, that empirically learn and correct pricing...

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and...

This paper studies modelling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for...

In this paper the performance of locally risk-minimizing hedge strategies for European options in stochastic volatility models is studied from an experimental as well as from an empirical perspective. These hedge strategies are derived for a large class of diffusion-type stochastic volatility...

This paper derives an analytic expression for the distribution of the average volatility in the stochastic volatility model of Hull and White. This result answers a longstanding question, posed by Hull and White (Journal of Finance 42, 1987), whether such an analytic form exists. Our findings...

We show that a simple equilibrium model with uncertain growth is able to simultaneously generate patterns in implied volatility and risk aversion that are similar to the ones observed in the data. In addition, the model produces an implied pricing kernel that is increasing for particular levels...

In this article, we describe the various sorts of American Parisian options and propose valuation formulae. Although there is no closed-form valuation for these products in the non perpetual case, we have been able to reformulate their price as a function of the exercise frontier. In the...

This paper studies modelling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in...

Institutional but also private investors have often limited flexibility in timing their investment decision. Therefore, they look for investments that would ideally be independent of the timing decision. We introduce a new class of derivative products whose payoff is linked to the trend of the...

This paper provides regime-switching stochastic volatility extensions of the LIBOR market model. First, the instantaneous forward LIBOR volatility is modulated by a continuous time homogeneous Markov chain. In a second parameterization, the volatility is modelled by a square root process with a...