Modified Black-Scholes Formula And Dynamic Hedging Strategy

To develop an option pricing and hedging method in incomplete market, and to improve the performance of the Black-Scholes formula in incomplete market, a Modified Black-Scholes formula and self-financing dynamic hedging strategy for European call option and put option was derived by mapping (S_T-K)_+â†'g((S_T-K)_+) and(K-S_T)_+â†'g((K-S_T)_+)in classic Black-Scholes framework. The modified method is toimprove the deficiency of classic Black-Scholes formula by taking into account the fat tail of the yield rate.With a well estimated GARCH model, By using stochastic simulation method we get the future stock index. And the dynamic hedging is performed both under modified Black-Scholes and the classic Black-Scholes framework. With the properly selected coefficient a_n, the Modified Black-Scholes model improves the average profit of the optionseller and reduces the risk measured by Value at Risk, compared with the classic Black-Scholes formula.