Mathematical Finance Seminar

May 1, 2003, 5:30 PM to 7:00 PM

Peter Carr, NYU

Robust Replication of Path Dependent Derivative Securities

Consider a contingent claim with a single payoff occuring at a fixed time which depends on the path of a single underlying asset. We give several examples of such payoffs which can be exactly replicated without assuming anything about the stochastic process governing the price of the underlying asset. We also consider super and sub replication and approximate replication. In general our replicating portfolios involve options both European and American. The trading strategies may be static, semi-static, or fully dynamic.