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Approximate Arbitrage

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  • Bernardo, Antonio
  • Ledoit, Olivier

Abstract

We propose a formal definition of approximate arbitrage which can be used to extend the applicability of theories based on the absence of arbitrage. Our definition is based on the radio of gain to loss, where gain (loss) is the expectation of the positive (negative) part of the excess payoff. Arbitrage is characterized by infinite gain-loss ratio, an approximate arbitrage by gain-loss ratio close to infinity. Our definition of approximate arbitrage has a use dual interpretation in terms of pricing kernels. This allows us to compare the pricing kernel restriction implied by a limit on the maximum gain-loss ration to the other in the literature. We show theoretically that only the gain-loss restriction is consistent with the absence of arbitrage and approximate arbitrage opportunities. We demonstrate the practical differences of these alternative pricing kernel restrictions by examining their implications for the prices of call options on an asset that does not trade.

Suggested Citation

  • Bernardo, Antonio & Ledoit, Olivier, 1999. "Approximate Arbitrage," University of California at Los Angeles, Anderson Graduate School of Management qt5dj834hk, Anderson Graduate School of Management, UCLA.
    • Handle: RePEc:cdl:anderf:qt5dj834hk
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    Cited by:

    1. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    2. Jordà, Òscar & Taylor, Alan M., 2012. "The carry trade and fundamentals: Nothing to fear but FEER itself," Journal of International Economics, Elsevier, vol. 88(1), pages 74-90.
    3. Huang, Yu-Lieh & Tsai, Jeffrey Tzuhao & Yang, Sharon S. & Cheng, Hung-Wen, 2014. "Price bounds of mortality-linked security in incomplete insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 30-39.

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