FX smile in the Heston model

Agnieszka Janek, Tino Kluge, Rafał Weron and Uwe Wystup

No 2010-047, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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.

Keywords: Heston model; vanilla option; stochastic volatility; Monte Carlo simulation; Feller condition; option pricing with FFT (search for similar items in EconPapers)
JEL-codes: C5 C63 G13 (search for similar items in EconPapers)
Date: 2010
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Related works:
Working Paper: FX Smile in the Heston Model (2010)
Working Paper: FX Smile in the Heston Model (2010)
Working Paper: FX Smile in the Heston Model (2010)
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