The Minimal Variance Hedging Strategy For European Options Under Martingale Approach

As we all known,as a derivative of the option to play a very important role in the management of financial risk.The hedging problem of the option is actually to solve the option of the seller to choose what kind of strategy,in order to avoid or reduce the possibility of selling options in the future may suffer losses.Many experts and scholars have also done a lot of research on option hedging,hoping to get the best effect of hedging risk through continuous exploration.In 1973,Black and Scholes put forward the Black-Scholes model of option pricing,which is referred to as BS model.Under some assumptions,the BS model is used to hedge the risk of the option by continuous trading of the underlying assets.However,a large number of statistical results show that the BS model is not consistent with the actual market price.Based on the assumption that the underlying asset discount process under the assumption that the geometric Brown motion,using the theory and method of martingale and stochastic analysis,studied the optimal hedging strategies for European options under the discrete state,the minimum variance hedging strategy:and the corresponding variance formula of hedging errorOn this basis,this paper uses the minimal variance hedging strategy and BS Delta hedging strategy,using empirical analysis method,the AAPL ATM option hedging risk comparative analysis.It is found that the minimum variance hedging strategy is always better than the Delta hedging strategy,especially in the long term and short hedging interval.Therefore,the minimal variance hedge ratio is an effective alternative to the standard BS Delta.