英文标题：
《Analytical and numerical results for American style of perpetual put
options through transformation into nonlinear stationary Black-Scholes
equations》
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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：
2017
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英文摘要：
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the nonlinear Black Scholes equation with a nonlinear volatility arises from option pricing models including, e.g., non-zero transaction costs, investors preferences, feedback and illiquid markets effects and risk from unprotected portfolio. We present a method how to transform the problem of American style of perpetual put options into a solution of an ordinary differential equation and implicit equation for the free boundary position. We finally present results of numerical approximation of the early exercise boundary, option price and their dependence on model parameters.
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中文摘要：
我们分析并计算了一类平稳广义Black-Scholes方程的早期行权边界，其中波动率函数依赖于期权价格本身的二阶导数。研究具有非线性波动率的非线性Black-Scholes方程的动机来自期权定价模型，包括非零交易成本、投资者偏好、反馈和非流动市场效应以及无保护投资组合的风险。我们提出了一种方法，将美式永久看跌期权问题转化为自由边界位置的常微分方程和隐式方程的解。最后，我们给出了早期行使边界、期权价格及其对模型参数依赖性的数值近似结果。
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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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