Speed and duration of drawdown under general Markov models
提出基于连续时间马尔可夫链近似的高效算法，计算一般一维马尔可夫过程回撤速度与持续时间的分布，并证明收敛性，应用于定价两种防范回撤风险的金融期权。
We propose an efficient computational method based on continuous-time Markov chain (CTMC) approximation to compute the distributions of the speed and duration of drawdown for general one-dimensional (1D) time-homogeneous Markov processes. We derive linear systems for the Laplace transforms of drawdown quantities and show how to solve them efficiently by recursion. In addition, we prove the convergence of our method and obtain a sharp estimate of the convergence rate under some assumptions. As applications, we consider pricing two financial options that provide protection against drawdown risk. Finally, we demonstrate the accuracy and efficiency of our method through extensive numerical experiments.