Coupling smiles

Valdo Durrleman and Nicole El Karoui

Quantitative Finance, 2008, vol. 8, issue 6, 573-590

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.

Keywords: Volatility modelling; Volatility surfaces; Stochastic volatility; Implied volatilities (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1080/14697680701691444

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