Hedging Options for a Large Investor and Forward-Backward SDE's

Abstract:     
The paper studies the problem of hedging European contingent claims in a continuous-time, generalized Black- Scholes-Merton model. Unlike the classical model, we allow price equations to be non-linear; moreover, the return rates and volatility parameters can depend on the wealth and portfolio strategy of the hedger, regarded therefore as a ``large investor". In mathematical terminology, the problem translates to solving a Forward-Backward Stochastic Differential Equation. The minimal hedging price and hedging strategy are given in terms of a solution to a nonlinear partial differential equation. Included in the examples is the case of the stock volatility increase caused by overpricing options on the stock. This increase can prevent the seller from being able to hedge all the risk.

JEL Classification: G13

working papers series