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FX BASKET OPTIONS - Approximation and Smile Prices

Karlsson, Patrik (2009)
Department of Economics
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... (More)
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. (Less)
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author
Karlsson, Patrik
supervisor
organization
year
type
H1 - Master's Degree (One Year)
subject
keywords
hedging, FX, Black-Scholes, Volatility Smile., Basket Option, Derivative, Local Volatility, Economics, econometrics, economic theory, economic systems, economic policy, Nationalekonomi, ekonometri, ekonomisk teori, ekonomiska system, ekonomisk politik
language
English
id
1436617
date added to LUP
2009-06-04 00:00:00
date last changed
2010-08-03 10:52:17
@misc{1436617,
  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.},
  author       = {Karlsson, Patrik},
  keyword      = {hedging,FX,Black-Scholes,Volatility Smile.,Basket Option,Derivative,Local Volatility,Economics, econometrics, economic theory, economic systems, economic policy,Nationalekonomi, ekonometri, ekonomisk teori, ekonomiska system, ekonomisk politik},
  language     = {eng},
  note         = {Student Paper},
  title        = {FX BASKET OPTIONS - Approximation and Smile Prices},
  year         = {2009},
}