Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations
The authors consider the valuation/hedging policies minimising the residual tracking error in discrete-time hedging. They evaluate the risk between trading dates through a function penalising profits and losses asymmetrically. After deriving the asymptotics from a discrete-time risk measurement for a large number of trading dates, they derive the optimal strategies minimising the asymptotic risk in a continuous-time setting. They characterise optimality through a class of fully nonlinear partial differential equations. Numerical experiments show that the optimal strategies associated with the discrete and the asymptotic approaches coincide asymptotically.
scientific article; zbMATH DE number 7227000
scientific article