13:00
: 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.