We price derivatives defined for different asset classes with a full stochastic dependence structure. We consider jointly geometric Brownian motions and mean-reversion processes with a a stochastic variance-covariance matrix driven by a Wishart process. These models cannot be treated within the...

We consider implied volatility, time-dependent volatility, local volatility and stochastic volatility. We derive relationships between the different concepts. The relationships are of an exact analytical type if this is possible, else we use expansions to obtain approximate expressions. We close...

We recall some fundamentals on Levy processes. Then the Gamma distribution, the Variance Gamma process and option pricing for this process are considered in detail. To implement the Variance Gamma model for option pricing, we use the fast Fourier transform, time change and discuss error bounds