Coupling smiles

Author: Durrleman Valdo   El Karoui Nicole  

Publisher: Routledge Ltd

ISSN: 1469-7688

Source: Quantitative Finance, Vol.8, Iss.6, 2008-09, pp. : 573-590

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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.