Consistent Pricing of Options on Leveraged ETFs

43 Pages Posted: 21 Sep 2012 Last revised: 22 Oct 2014

See all articles by Andrew Ahn

Andrew Ahn

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Martin B. Haugh

Imperial College Business School

Ashish Jain

Independent

Date Written: October 2014

Abstract

We consider the problem of pricing options on a leveraged ETF (LETF) and the underlying ETF in a consistent manner. We show that if the underlying ETF has Heston dynamics then the LETF also has Heston dynamics so that options on both the ETF and the LETF can be priced analytically using standard transform methods. If the underlying ETF has tractable jump-diffusion dynamics then the dynamics of the corresponding LETF are generally intractable in that we cannot compute a closed-form expression for the characteristic function of the log-LETF price. In that event we propose tractable approximations based on either moment-matching techniques or saddlepoint approximations to the LETF price dynamics under which the characteristic function of the log-LETF price can be found in closed form. In a series of numerical experiments including both low and high volatility regimes, we show that the resulting LETF option price approximations are very close to the true prices which we calculate via Monte-Carlo. Because approximate LETF option prices can be computed very quickly our methodology should be useful in practice for pricing and risk-managing portfolios that contain options on both ETFs and related LETFs. Our numerical results also demonstrate the model-dependency of LETF option prices and this is particularly noticeable in high-volatility environments.

Keywords: ETFs, leveraged ETFs, options

JEL Classification: C44, C65, G12, G13

Suggested Citation

Ahn, Andrew and Haugh, Martin B. and Jain, Ashish, Consistent Pricing of Options on Leveraged ETFs (October 2014). Available at SSRN: https://ssrn.com/abstract=2149736 or http://dx.doi.org/10.2139/ssrn.2149736

Andrew Ahn

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Martin B. Haugh (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

Ashish Jain

Independent ( email )

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