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Coupling smiles

Author

Listed:
  • Valdo Durrleman
  • Nicole El Karoui

Abstract

The present paper addresses the problem of computing implied volatilities of options written on a domestic asset based on implied volatilities of options on the same asset expressed in a foreign currency and the exchange rate. It proposes an original method together with explicit formulae to compute the at-the-money implied volatility, the smile's skew, convexity, and term structure for short maturities. The method is completely free of any model specification or Markov assumption; it only assumes that jumps are not present. We also investigate how the method performs on the particular example of the currency triplet dollar, euro, yen. We find a very satisfactory agreement between our formulae and the market at one week and one month maturities.

Suggested Citation

  • Valdo Durrleman & Nicole El Karoui, 2008. "Coupling smiles," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 573-590.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:6:p:573-590
    DOI: 10.1080/14697680701691444
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    Cited by:

    1. Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.

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