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February 2019 Robust hedging of options on a leveraged exchange traded fund
Alexander M. G. Cox, Sam M. Kinsley
Ann. Appl. Probab. 29(1): 531-576 (February 2019). DOI: 10.1214/18-AAP1427

Abstract

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 characterising 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.

Citation

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Alexander M. G. Cox. Sam M. Kinsley. "Robust hedging of options on a leveraged exchange traded fund." Ann. Appl. Probab. 29 (1) 531 - 576, February 2019. https://doi.org/10.1214/18-AAP1427

Information

Received: 1 February 2017; Revised: 1 February 2018; Published: February 2019
First available in Project Euclid: 5 December 2018

zbMATH: 07039132
MathSciNet: MR3910011
Digital Object Identifier: 10.1214/18-AAP1427

Subjects:
Primary: 60G40, 91G20
Secondary: 60G44, 60J60

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 1 • February 2019
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