Pricing American drawdown options under Markov models

Xiang Zhang, Lingfei Li and Gongqiu Zhang

European Journal of Operational Research, 2021, vol. 293, issue 3, 1188-1205

Abstract: The drawdown in the price of an asset shows how much the price falls relative to its historical maximum. This paper considers the pricing problem of perpetual American style drawdown call options, which allow the holder to optimally choose the time to receive a call payoff written on the drawdown. Our pricing framework includes classical Russian options and American lookback puts as special cases after a suitable equivalent measure change. We approximate the original asset price model by a continuous time Markov chain and develop two types of algorithms to solve the optimal stopping problem for the drawdown process. The first one is a transform based algorithm which is applicable to general exponential Lévy models. The second approach solves the linear complementarity problem (LCP) associated with the variational inequalities for the value function and it applies to general Markov models. We propose an efficient Block-LCP (BLCP) method that reduces an LCP with big size to a sequence of sub-LCPs with mild size which can be solved by a variety of LCP solvers and we identify the best solver through numerical experiments. Convergence of Markov chain approximation is proved and various numerical examples are given to demonstrate their computational efficiency and convergence properties. An extension of the BLCP method to the finite maturity case is also provided.

Keywords: Finance; Drawdown; Optimal stopping; Markov chain approximation; Linear complementarity problem (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:293:y:2021:i:3:p:1188-1205

DOI: 10.1016/j.ejor.2021.01.033

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