We explain the valuation and correlation hedging of Foreign Exchange Basket Options in a multi-dimensional Black-Scholes model that allows including the smile. The technique presented is a fast analytic approximation to an accurate solution of the valuation problem.

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...

The vanna-volga method, also called the traders' rule of thumb is an empirical procedure that can be used to infer an implied-volatility smile from three available quotes for a given maturity. It is based on the construction of locally replicating portfolios whose associated hedging costs are...

A quanto option can be any cash-settled option, whose payoff is converted into a third currency at maturity at a pre-specified rate, called the quanto factor. There can be quanto plain vanilla, quanto barriers, quanto forward starts, quanto corridors, etc. The valuation theory is covered for...