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.