Mathematical Finance Seminar

April 11, 2002 5:30 PM to 7:00 PM

Thomas F. Coleman, Cornell University

Discrete Hedging Under Piecewise Linear Risk Minimization

In an incomplete market it is impossible to eliminate the intrinsic risk of an option that cannot be replicated. In this case quadratic risk-minimization is often used to determine a hedging strategy. However, it may be more natural to use a piecewise linear risk-minimization since in this case the risk is measured in actual dollars (not dollars squared!). Moreover, less attention is paid to low probability events when piecewise linear risk-minimization is used. In this talk we illustrate that piecewise linear risk minimization often leads to smaller expected total hedging cost and risk; more desirable hedging strategies are produced. Comparative numerical results are provided.