The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 29, Number 1 (2019), 531-576.
Robust hedging of options on a leveraged exchange traded fund
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.
Ann. Appl. Probab., Volume 29, Number 1 (2019), 531-576.
Received: February 2017
Revised: February 2018
First available in Project Euclid: 5 December 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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