Optimal partial hedging of an American option: shifting the focus to the expiration date
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.
scientific article; zbMATH DE number 6137600