Energy Estimation Of The Black-Scholes Equation And Its Application Of Option Pricing

In this article, we use the standard energy method to get a local estimationof the equation:on [0, T]×[0, +∞) and under the estimation we give a range of options' value:and on eachΩ_i = {S|(i - i)△S≤S≤i△S}, we haveg(S) is the stationary solution of the equation;Although we can get the exact solution of Black-Scholes (B-S) equation which is the theoretic price of European option, the equation is derived under some ideal hypotheses. In applications of reality, there are some defects. Taking this into account, we consider a reasonable interval of options but not a exact value. The result is significant in practical application of pricing of options and hedging.