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Title:FX smile in the Heston model PDF Logo
Authors:Janek, Agnieszka
Kluge, Tino
Weron, Rafał
Wystup, Uwe
Issue Date:2010
Series/Report no.:SFB 649 discussion paper 2010-047
Abstract:The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical solution for European options. In this article we adapt the original work of Heston (1993) to a foreign exchange (FX) setting. We discuss the computational aspects of using the semi-analytical formulas, performing Monte Carlo simulations, checking the Feller condition, and option pricing with FFT. In an empirical study we show that the smile of vanilla options can be reproduced by suitably calibrating three out of five model parameters.
Subjects:Heston model
vanilla option
stochastic volatility
Monte Carlo simulation
Feller condition
option pricing with FFT
JEL:C5
C63
G13
Document Type:Working Paper
Appears in Collections:SFB 649 Discussion Papers, HU Berlin

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