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 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...

This paper addresses the issue of intergenerational and international sharing of longevity and growth risks. Current research on worldwide demographic changes highlights the importance of longevity risk on financial markets and the need to devise optimal hedging vehicles. We present a potential...