  In this paper, we address the question of the optimal Delta and Vega hedging
of a book of exotic options when there are execution costs associated with the
trading of vanilla options. In a framework where exotic options are priced
using a market model (e.g. a local volatility model recalibrated continuously
to vanilla option prices) and vanilla options prices are driven by a stochastic
volatility model, we show that, using simple approximations, the optimal
dynamic Delta and Vega hedging strategies can be computed easily using
variational techniques.
