Coupling Smiles

26 Pages Posted: 7 Aug 2007

See all articles by Valdo Durrleman

Valdo Durrleman

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS

Nicole El Karoui

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Date Written: March 20, 2007

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 formulas 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 formulas and the market at one week and one month maturities.

Keywords: Implied volatility, foreign exchange options.

JEL Classification: G13

Suggested Citation

Durrleman, Valdo and El Karoui, Nicole, Coupling Smiles (March 20, 2007). Available at SSRN: https://ssrn.com/abstract=1005332 or http://dx.doi.org/10.2139/ssrn.1005332

Valdo Durrleman (Contact Author)

Ecole Polytechnique - Centre de Mathematiques Appliquees - CNRS ( email )

Palaiseau, 91128
France

Nicole El Karoui

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France
(33) 1 69 33 41 48 (Phone)
(33) 1 69 33 70 31 (Fax)

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