Patrik Karlsson

FX BASKET OPTIONS
- Approximation and Smile Prices -

Abstract
Pricing a Basket option for Foreign Exchange (FX) both with Monte Carlo
(MC) techniques and built on different approximation techniques matching
the moments of the Basket option. The thesis is built on the assumption
that each underlying FX spot can be represented by a geometric Brownian
motion (GBM) and thus have log normally distributed FX returns. The
values derived from MC and approximation are thereafter priced in a such
a way that the FX smile effect is taken into account and thus creating
consistent prices. The smile effect is incorporated in MC by assuming
that the risk neutral probability and the Local Volatility can be
derived from market data, according to Dupire (1994). The approximations
are corrected by creating a replicated portfolio in such a way that this
replicated portfolio captures the FX smile effect.