Coupling smiles

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.