Calibration and Vega of Exotic Derivative Pricing Models
Dr Thomas Knudsen, Abbey National

Abstract:
Most interest rate models and several models for pricing equity and FX options postulate a stochastic evolution of the state variables where the equations for the evolution are parametrised by a number of unobservable parameters. These parameters are then determined by calibrating the model to a set of liquid market instruments. Specific models include HJM/BGM and Hull-White for interest rate derivatives and the Heston model in equity/FX. Traditionally the vega of these models is the price sensitivity with respect to certain of these parameters. This vega is standard output from the models. However, these model vegas do not depend on the calibration. So the way market moves are transformed into model moves does not influence the model vega. This suggests that simply hedging model vega is insufficient. Furthermore, calculation of Value at Risk (VaR) requires time series of the (unobservable) parameters. Hence both for hedging and VaR, it is desirable to be able to calculate the sensitivity of the model price with respect to the market instruments. This seminar shows how it is possible to transform model vega into market vega and further explores the properties of the different ways of hedging vega.