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引用次数: 1
摘要
Black Scholes(B-S)模型是计算期权价格的常用方法之一。它由线性Black Scholes方程的封闭形式解组成。研究人员还发现了Black Scholes方程的数值解,它比封闭形式的解更直观。本文比较了控制期权定价的线性Black-Scholes方程的解析解和数值解。利用有限差分法(FDMs)对B-S方程进行了显式、隐式和曲克尼克尔森三种不同格式的离散化。我们还试图找出这个解决方案是否有效,以计算更高的执行价格的期权,如BANKNIFTY期权的价格。数值解与网格数无关。
A comparison between analytic and numerical solution of linear Black-Scholes equation governing option pricing: Using BANKNIFTY
Black Scholes(B-S) model is one of the popular methods of calculating the option prices. It consists of the closed form solution of the linear Black Scholes equation. Researchers have also found the numerical solutions of the Black Scholes equation which is much more intuitive compared to its closed form solution. In this paper, we have compared the analytical solution with the numerical solution of linear Black-Scholes equation governing option pricing. Finite Difference methods (FDMs) are used to discretize B-S equation base on three different schemes namely, Explicit, Implicit and the Crank Nicholson scheme. We have also tried to found out whether this solution are validate to compute the price the options of the higher strike prices such as those of BANKNIFTY options. It is also showed that numerical solutions are independent of number of grids.