In this paper we propose a transform method to compute the prices and Greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Levy model with...

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 pre-specified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from...

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...

In this paper, we develop an algorithm to calculate the prices and Greeks of barrier options in a hyper-exponential additive model with piecewise constant parameters. We obtain an explicit semi-analytical expression for the first-passage probability. The solution rests on a randomization and an...

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...