论文标题
在时间依赖的Ornstein Uhlenbeck过程上写的屏障和美国选项的半密闭形式解决方案
Semi-closed form solutions for barrier and American options written on a time-dependent Ornstein Uhlenbeck process
论文作者
论文摘要
在本文中，我们为屏障（也许是时间依赖）和在基础股票上写的美国选项开发了半锁定的形式解决方案，该解决方案遵循具有对数正态漂移的时间依赖性OU过程。该模型等同于FI中熟悉的船体白色模型，或FX中的时间依赖性OU模型。半关闭形式意味着，给定时间依赖的利率，连续股息和波动率函数，需要在数值上求解第一类的线性（用于屏障选项）或非线性（用于美国选项）的弗雷德霍尔姆方程。之后，所有情况下的期权价格均以上述解决方案和Jacobi Theta功能组合的一维积分呈现。我们还证明，计算上我们的方法比用于解决这些问题的向后有限差方法更有效，并且也可以像前向有限差求解器一样有效，同时提供更好的准确性和稳定性。
In this paper we develop a semi-closed form solutions for the barrier (perhaps, time-dependent) and American options written on the underlying stock which follows a time-dependent OU process with a log-normal drift. This model is equivalent to the familiar Hull-White model in FI, or a time dependent OU model in FX. Semi-closed form means that given the time-dependent interest rate, continuous dividend and volatility functions, one need to solve numerically a linear (for the barrier option) or nonlinear (for the American option) Fredholm equation of the first kind. After that the option prices in all cases are presented as one-dimensional integrals of combination of the above solutions and Jacobi theta functions. We also demonstrate that computationally our method is more efficient than the backward finite difference method used for solving these problems, and can also be as efficient as the forward finite difference solver while providing better accuracy and stability.
