Speed and duration of drawdown under general Markov models (Q6576880)

In this study, the authors analyze the speed and duration of drawdown for 1D time-homogeneous Markov processes. The goal is to develop a computational method that is applicable to general models, whereas the existing papers only considered some specific classes of processes. To this end, the authors employ the method of continuous-time Markov chain (CTMC) approximation, which has proven to be powerful for solving various problems in applied probability under general Markov models.\N\NThe idea is to approximate the original Markov process living on a continuous state space by a CTMC, which lives on a discrete state space. The authors solve the problem for the CTMC and use the solution to approximate the solution of the original model. This approach has been taken to develop computationally efficient algorithms for various problems in applied probability and financial engineering. \NAs applications, pricing two financial options that provide protection against drawdown risk is considered. Finally, the accuracy and efficiency of the method through extensive numerical experiments are demonstrated.