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FX Smile in the Heston Model

Author

Listed:
  • Agnieszka Janek
  • Tino Kluge
  • Rafal Weron
  • Uwe Wystup

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.

Suggested Citation

  • Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    • Handle: RePEc:wuu:wpaper:hsc1002
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    More about this item

    Keywords

    Heston model; vanilla option; stochastic volatility; Monte Carlo simulation; Feller condition; option pricing with FFT;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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