Optimal partial hedging of an American option: shifting the focus to the expiration date
type: Item
instance of: scholarly article
title: Optimal partial hedging of an American option: shifting the focus to the expiration date
zbMATH Open document ID: 1267.91075
author: Peter Lindberg
published in: Mathematical Methods of Operations Research
publication date: 2013-02-20T00:00:00Z
review text: The paper studies partial (resp.\ quantile) hedging both for European and American options in discrete complete stock markets as e.g.\ the binomial model. More specifically, the goal is to hedge the option perfectly with probability \(1-\varepsilon\) while bounding possible terminal losses by \(-c\). For European options, market completeness implies that the problem reduces to determining the cheapest strategy with positive wealth process whose terminal value exceeds \(c\) with probability \(1-\varepsilon\). If the probability of all atoms is small, it is approximately optimal to invest in the replicating strategy of the Arrow-Debreu securities with smallest likelihood ratio \(dP^*/dP\), i.e.\ in the relatively cheap atoms. In the American case, perfect replication with probability \(1-\varepsilon\) and boundedness of terminal losses by \(-c\) are required for all possible stopping times of the holder. The structure of the solution is similar to the European case. The paper concludes with a numerical study.
reviewed by: Jan Kallsen
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 91G60
zbMATH DE Number: 6137600
zbMATH Keywords: quantile hedging
zbMATH Keywords: American options
zbMATH Keywords: knapsack problem
zbMATH Keywords: greedy algorithm
zbMATH Keywords: binomial model
MaRDI profile type: Publication
full work available at URL: s00186-012-0382-9
OpenAlex ID: W2009306143
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DOI: 10.1007/S00186-012-0382-9
description: scientific article; zbMATH DE number 6137600