Hedging Options On Exploding Exchange Rates

: Recently strict local martingales have been used to model

exchange rates. In such models, put-call parity does not hold if one

assumes minimal superreplicating costs as contingent claim prices. I

will illustrate how put-call parity can be restored by changing the

definition of a contingent claim price.

More precisely, I will discuss a change of numeraire technique when the

underlying is only a local martingale. Then, the new measure is not

necessarily equivalent to the old measure. If one now defines the price

of a contingent claim as the minimal superreplicating costs under both

measures, then put-call parity holds. I will discuss properties of this

new pricing operator.

To illustrate this techniques, I will discuss the class of "Quadratic

Normal Volatility" models, which have drawn much attention in the

financial industry due to their analytic tractability and flexibility.

This talk is based on joint work with Peter Carr and Travis Fisher.