Perpetual American options in diffusion-type models with running maxima and drawdowns
Perpetual American options in diffusion-type models with running maxima and drawdowns
复制标题
具有运行最大值和回撤的扩散型模型的永久美式期权
DOI：
10.1016/j.spa.2016.01.003
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发表时间：
2016
影响因子：
1.4
通讯作者：
Neofytos Rodosthenous
中科院分区：
文献类型：
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作者：
P. Gapeev;Neofytos Rodosthenous
本文研究了基于Black-Merton-Scholes模型的永久美式期权定价问题，其中标的风险资产的股息率和波动率取决于其最大和最大回降的运行值。根据相关的最大和最大递减过程的运行值，显示的最佳运行时间是基础资产达到某些边界的第一次。对三维马尔可夫过程的最优停止边界光滑拟合和状态空间边缘法向反射的值函数，得到了等效自由边界问题的闭型解。用一类一阶非线性常微分方程的最小解确定了具有固定行权和浮动行权的永久美式期权在市场深度最大值上的最优行权边界。
We study perpetual American option pricing problems in an extension of the Black–Merton–Scholes model in which the dividend and volatility rates of the underlying risky asset depend on the running values of its maximum and maximum drawdown. The optimal exercise times are shown to be the first times at which the underlying asset hits certain boundaries depending on the running values of the associated maximum and maximum drawdown processes. We obtain closed-form solutions to the equivalent free-boundary problems for the value functions with smooth fit at the optimal stopping boundaries and normal reflection at the edges of the state space of the resulting three-dimensional Markov process. The optimal exercise boundaries for the perpetual American options on the maximum of the market depth with fixed and floating strikes are determined as the minimal solutions of certain first-order nonlinear ordinary differential equations.