Quadratic Hedging for Contingent Claims with Delta Constraint

ABSTRACT In this paper, under constraint of delta-strategy and by importing another related risky asset to compose a hedging portfolio comprising the underlying asset and riskless asset(the Bond). Firstly, we excellently devise a dynamic hedging program for contingent claims; and then, according to Principle of Dynamic Programming and by taking advantage of backward recursion technique, at each rebalance moment before option’s maturity date, the optimal hedging strategies are acquired to (1) eliminate the diffusion risk by imposing delta constraint; and (2) depress the jump risk using the hedging portfolio, which minimize the mean squared error between the terminal valuation of hedging portfolio and the payment obligation that the option issuer may be charged with; lastly, at the end of this paper, empirical analysis and numerical results indicate that our proposed hedging strategy is not only efficacious and feasible but also convenient and simple to manipulate, at the same time, it is referential to hedging practice.