A Markov chain with an expanding non-uniform grid matching risk neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with prespecified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from...

We construct a dynamical credit model that can be calibrated exactly to CDS quotes. Modelling the default time as the first-passage time of a credit index process to the level zero, we show that the parameters of this credit index process can be chosen such that the risk-neutral (implied)...

We present a new numerical method to price vanilla options in time-changed Brownian motion models quickly. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a number of widely used models. In particular, we use the...

In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of...

With an interest in keeping the cost of carry at acceptable levels for the expression of a positive or negative view on an equity asset over the longer term, a variation to equity default swaps is introduced that fixes the barrier at a given quantile. The barrier level for the stock price then...

Eberlein, Kallsen and Kristen (2003) argued that the VIX index is a good way to devolatize SPX returns. Adopting this approach we construct a risk neutral model for SPX returns as a variance gamma process scaled by the VIX. We model the risk neutral evolution of the squared VIX as a mean...