Consistent Pricing of Options on Leveraged ETFs
Columbia University - Department of Industrial Engineering and Operations Research (IEOR); Columbia University - Center for Financial Engineering
Columbia University - Department of Industrial Engineering and Operations Research (IEOR)
September 20, 2012
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. Instead we propose tractable 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.
Number of Pages in PDF File: 42
Keywords: ETFs, levergaed ETFs, options
JEL Classification: C44, C65, G12, G13working papers series
Date posted: September 21, 2012 ; Last revised: July 22, 2013
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