英文标题：
《Pricing American Call Options by the Black-Scholes Equation with a
Nonlinear Volatility Function》
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作者：
Maria do Rosario Grossinho, Yaser Faghan Kord, Daniel Sevcovic
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最新提交年份：
2018
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英文摘要：
In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a numerical method for pricing American style call options by means of transformation of the free boundary problem for a nonlinear Black-Scholes equation into the so-called Gamma variational inequality with the new variable depending on the Gamma of the option. We apply a modified projective successive over relaxation method in order to construct an effective numerical scheme for discretization of the Gamma variational inequality. Finally, we present several computational examples for the nonlinear Black-Scholes equation for pricing American style call option under presence of variable transaction costs.
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中文摘要：
本文研究了美式看涨期权定价的Black-Scholes方程的非线性推广，其中波动率项可能取决于基础资产价格和期权的伽马。我们提出了一种美式看涨期权定价的数值方法，通过将非线性Black-Scholes方程的自由边界问题转化为所谓的Gamma变分不等式，新变量取决于期权的Gamma。为了构造伽玛变分不等式离散化的有效数值格式，我们采用了一种改进的投影逐次超松弛方法。最后，我们给出了在交易成本可变的情况下，美式看涨期权定价的非线性Black-Scholes方程的几个计算实例。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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