论文标题
选项定价在路径依赖的库存模型下
Option pricing under path-dependent stock models
论文作者
论文摘要
本文研究了如何以路径依赖性SDE解决方案给出的股票模型下的价格和对冲期权。当路径依赖性的SDE系数具有FRéchet衍生物时，期权价格相对于时间和路径是可区分的，并且作为对路径依赖性PDE的解决方案。这可以被视为Feynman-kac公式的路径依赖性版本。作为副产品，我们获得了依赖路径依赖性SDE溶液的不同性和其衍生物的SDE表示。此外，我们为具有路径依赖系数扰动的希腊人提供公式。涵盖了具有带有时间集成形式的路径的系数的库存模型。
This paper studies how to price and hedge options under stock models given as a path-dependent SDE solution. When the path-dependent SDE coefficients have Fréchet derivatives, an option price is differentiable with respect to time and the path, and is given as a solution to the path-dependent PDE. This can be regarded as a path-dependent version of the Feynman-Kac formula. As a byproduct, we obtain the differentiability of path-dependent SDE solutions and the SDE representation of their derivatives. In addition, we provide formulas for Greeks with path-dependent coefficient perturbations. A stock model having coefficients with time integration forms of paths is covered as an example.
