考虑交易费的欧式看涨期权定价的数值解

在过去20年里,非线性的Black-Scholes方程已越来越多地引起人们的注意,因为他们考虑到更现实的假设,如交易成本,来自未受保护的资产组合的风险,大型投资者的偏好或流动性市场(这可能会影响到股票价格)的波动率,漂移率和期权本身的价格,从而为期权定价提供了更为准确的方法。在本文中,我们将侧重于一类带有波动率模型的欧式期权的非线性的Black-Scholes方程,其中波动率取决于不同的因素,如股票价格,时间,期权价格和交易成本.对欧式期权来说就是把这个问题转化成带有一个非线性项的对流扩散方程来逼近期权的价格。最后,我们将给出带有各种波动率模型(包括利兰模型和BoyleVorst模型)的欧式期权定价的数值解。

The past 20 years,nonlinear Black-Scholes equation has been increasingly attracting attention,because they take into account more realistic assumptions,such as transaction costs and risks of unprotected portfolio preferences of large investors or market illiquidity(which may affect the stock price) volatility,drift rate and the option itself prices,thus providing a more accurate value.In this paper,we will focus on a class of model with a volatility of European options nonlinear Black-Scholes equation,which depends on the volatility of different factors,such as stock price,time,options prices and transaction costs.Of the European option is to run into this problem with a nonlinear convection-diffusion equation of the approximation to the price of options.Finally,we will give a variety of fluctuations in the model(including the Leland model and Boyle-Vorst pricing model) of the European option values of the different results of the discrete method.