This paper investigates risk-neutral price of European option under dividend barrier strategy when cumulative log-return during time interval [0,t] of the underlying stock in the absence of dividends follows a Brownian motion with drift. Such a dividend barrier strategy means that in 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...

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...

In this paper we present a fast and accurate algorithm for pricing barrier options in one-dimensional Markov models, including general local volatility models with jumps, L\'evy processes and L\'evy driven SDEs. The approach rests on the construction of an approximating continuous-time Markov...