A general method for analysis and valuation of drawdown risk

Abstract

Drawdown risk is a major concern in financial markets. We develop a novel method to solve the first passage problem of the drawdown process for general one-dimensional Markov processes (including time-inhomogeneous ones) as well as regime-switching and stochastic volatility models. We compute its Laplace transform based on continuous-time Markov chain (CTMC) approximation and invert the Laplace transform numerically to obtain the first passage probabilities and the distribution of the maximum drawdown. We prove convergence of our method for general Markov models and provide sharp estimate of the convergence rate for a general class of jump-diffusion models. We apply our method to price and hedge maximum drawdown options and demonstrate its accuracy and efficiency through various numerical experiments. In addition, we can apply our method to calculate the Calmar ratio for investment analysis, and quantify the contributions of assets to the drawdown risk of a portfolio when the assets follow multivariate exponential Lévy models.