Robust Hedging of Options on a Leveraged Exchange Traded Fund

Alexander M. G. Cox, Sam M. Kinsley

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A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options. To obtain an upper bound, we establish a new optimal solution to the Skorokhod embedding problem (SEP) using methods introduced in Beiglböck–Cox–Huesmann. This stopping time can be represented as the hitting time of some region by a Brownian motion, but unlike other solutions of, for example, Root, this region is not unique. Much of this paper is dedicated to character-ising the choice of the embedding region that gives the required optimality property. Notably, this appears to be the first solution to the SEP where the solution is not uniquely characterised by its geometric structure, and an additional condition is needed on the stopping region to guarantee that it is the optimiser. An important part of determining the optimal region is identifying the correct form of the dual solution, which has a financial interpretation as a model-independent superhedging strategy.

Original languageEnglish
Pages (from-to)531-576
Number of pages46
JournalAnnals of Applied Probability
Issue number1
Early online date5 Dec 2018
Publication statusPublished - 1 Feb 2019


  • Leveraged exchange traded fund
  • Monotonicity principle
  • Optimal Skorokhod embedding problem
  • Robust pricing and Hedging

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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