The Annals of Applied Probability

Robust hedging of options on a leveraged exchange traded fund

Alexander M. G. Cox and Sam M. Kinsley

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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.

Article information

Source
Ann. Appl. Probab., Volume 29, Number 1 (2019), 531-576.

Dates
Received: February 2017
Revised: February 2018
First available in Project Euclid: 5 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1544000436

Digital Object Identifier
doi:10.1214/18-AAP1427

Mathematical Reviews number (MathSciNet)
MR3910011

Zentralblatt MATH identifier
07039132

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 91G20: Derivative securities
Secondary: 60G44: Martingales with continuous parameter 60J60: Diffusion processes [See also 58J65]

Keywords
Leveraged exchange traded fund optimal Skorokhod embedding problem monotonicity principle robust pricing and hedging

Citation

Cox, Alexander M. G.; Kinsley, Sam M. Robust hedging of options on a leveraged exchange traded fund. Ann. Appl. Probab. 29 (2019), no. 1, 531--576. doi:10.1214/18-AAP1427. https://projecteuclid.org/euclid.aoap/1544000436


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