A key requirement of any equity hybrid derivatives pricing model is the ability to rapidly and accurately calibrate to vanilla option prices. To this end, we present two methods for calibrating a local volatility model under correlated stochastic interest rates. This is achieved by first fitting a mixture model to market prices, and then determining the local volatility function that is consistent with this mixture model.

As observed by Carr and Lee (2009), variance swaps and other more complex volatility derivatives are increasingly being used by organizations to either trade volatility or hedge their portfolio’s v...