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Keywords:

  • VaR;
  • Monte Carlo;
  • option implied distribution

Abstract

The foreign exchange options market is one of the largest and most liquid OTC derivative markets in the world. Surprisingly, very little is known in the academic literature about the construction of the most important object in this market: The implied volatility smile. The smile construction procedure and the volatility quoting mechanisms are FX specific and differ significantly from other markets. We give a brief overview of these quoting mechanisms and provide a comprehensive introduction to the resulting smile construction problem. Furthermore, we provide a new formula which can be used for an efficient and robust FX smile construction.