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Short-Time Expansions for Call Options on Leveraged ETFs Under Exponential L\'evy models With Local Volatility

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Listed:
  • Jos'e E. Figueroa-L'opez
  • Ruoting Gong
  • Matthew Lorig

Abstract

In this article, we consider the small-time asymptotics of options on a \emph{Leveraged Exchange-Traded Fund} (LETF) when the underlying Exchange Traded Fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. Our main results are closed-form expressions for the leading order terms of off-the-money European call and put LETF option prices, near expiration, with explicit error bounds. We show that the price of an out-of-the-money European call on a LETF with positive (negative) leverage is asymptotically equivalent, in short-time, to the price of an out-of-the-money European call (put) on the underlying ETF, but with modified spot and strike prices. Similar relationships hold for other off-the-money European options. In particular, our results suggest a method to hedge off-the-money LETF options near expiration using options on the underlying ETF. Finally, a second order expansion for the corresponding implied volatility is also derived and illustrated numerically.

Suggested Citation

  • Jos'e E. Figueroa-L'opez & Ruoting Gong & Matthew Lorig, 2016. "Short-Time Expansions for Call Options on Leveraged ETFs Under Exponential L\'evy models With Local Volatility," Papers 1608.07863, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1608.07863
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    1. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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