Clarence Simard, Université du Québec à Montréal (UQAM)

Title: Some practical and less practical results on quadratic hedging

Abstract: The quadratic hedging portfolio minimizes the expected squared difference between the value of the hedging portfolio and the contingent claim at maturity. This quadratic penalty has a drawback since values of the portfolio greater or smaller than the contingent claim are equally penalized. On the other hand, solutions for the quadratic hedging portfolio come from the L2-space projection which forbid asymmetrical penalties. For the first part of this talk, I will present a modification of the quadratic hedging portfolio which leads to a hedging portfolio with expected value greater than the contingent claim while keeping tractability of the quadratic hedging portfolio. The quadratic hedging theory is only valid for perfectly liquid market models since the value of the portfolio must be a linear function of the trading strategy. Consequently, this theory cannot be used for illiquid market models such as limit order book models. For this second part of the talk, I will present an extension of the martingale representation for nonlinear stochastic integrals and discuss the possible application to quadratic hedging for illiquid market models.