A General Method for Valuation of Drawdown Risk under Markov Models

Speaker: Lingfei Li from Chinese University of Hong Kong

Time: 10/8/2020, 9am-9:50am

Abstract: We develop a novel algorithm for the analysis of drawdown in general one-dimensional Markovian models. We compute the Laplace transform of the first passage time of the drawdown process based on continuous time Markov chain (CTMC) approximation and numerically invert the Laplace transform to obtain first passage probabilities of drawdown and the distribution of maximum drawdown. Our method has important applications in financial markets where drawdown risk is a major concern and we apply it to price and hedge several types of drawdown derivatives. We prove convergence of our algorithm for general Markovian models and provide sharp estimates of the convergence rates for a general class of jump-diffusion models. Various numerical experiments document the computational efficiency of our method and its advantages over popular alternatives. In an empirical study on bitcoin, we show that some drawdown derivatives can adequately safeguard extreme price risk and that a dynamic hedging strategy can effectively hedge the risk of selling drawdown derivatives. Extensions of our method to analyze drawdown problems in models with time dependence or stochastic volatility or regime switching as well as to quantify portfolio-level drawdown risk are also provided.

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