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FX Smile in the Heston Model

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  • Janek, Agnieszka
  • Kluge, Tino
  • Weron, Rafal
  • Wystup, Uwe

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 non-negative 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.

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  • Janek, Agnieszka & Kluge, Tino & Weron, Rafal & Wystup, Uwe, 2010. "FX Smile in the Heston Model," MPRA Paper 25491, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:25491
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    Cited by:

    1. Olena Burkovska & Maximilian Ga{ss} & Kathrin Glau & Mirco Mahlstedt & Wim Schoutens & Barbara Wohlmuth, 2016. "Calibration to American Options: Numerical Investigation of the de-Americanization," Papers 1611.06181, arXiv.org.
    2. Janek, Agnieszka, 2011. "The vanna - volga method for derivatives pricing," MPRA Paper 36127, University Library of Munich, Germany.
    3. Yiran Cui & Sebastian del Ba~no Rollin & Guido Germano, 2015. "Full and fast calibration of the Heston stochastic volatility model," Papers 1511.08718, arXiv.org, revised May 2016.
    4. Nicole Wiebach & Lutz Hildebrandt, 2010. "Context Effects as Customer Reaction on Delisting of Brands," SFB 649 Discussion Papers SFB649DP2010-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500078 is not listed on IDEAS
    6. Oliver Pfante & Nils Bertschinger, 2016. "Uncertainty Estimates in the Heston Model via Fisher Information," Papers 1610.04760, arXiv.org, revised Oct 2016.
    7. 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.
    8. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121.
    9. Alexander Lipton & Andrey Gal & Andris Lasis, 2013. "Pricing of vanilla and first generation exotic options in the local stochastic volatility framework: survey and new results," Papers 1312.5693, arXiv.org.
    10. Elisa Alòs & Rafael De Santiago & Josep Vives, 2012. "Calibration of stochastic volatility models via second order approximation: the Heston model case," Economics Working Papers 1346, Department of Economics and Business, Universitat Pompeu Fabra.
    11. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
    12. Franziska Schulze, 2010. "Spatial Dependencies in German Matching Functions," SFB 649 Discussion Papers SFB649DP2010-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Technology.
    14. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    15. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Enno Mammen & Christoph Rothe & Melanie Schienle, 2010. "Nonparametric Regression with Nonparametrically Generated Covariates," SFB 649 Discussion Papers SFB649DP2010-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. repec:wsi:ijtafx:v:18:y:2015:i:06:n:s0219024915500363 is not listed on IDEAS
    18. Marjon Ruijter & Kees Oosterlee, 2012. "Two-dimensional Fourier cosine series expansion method for pricing financial options," CPB Discussion Paper 225, CPB Netherlands Bureau for Economic Policy Analysis.
    19. Ralf Sabiwalsky, 2010. "Executive Compensation Regulation and the Dynamics of the Pay-Performance Sensitivity," SFB 649 Discussion Papers SFB649DP2010-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    20. Antoine Jacquier & Aleksandar Mijatović, 2014. "Large Deviations for the Extended Heston Model: The Large-Time Case," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(3), pages 263-280, September.
    21. Vladimir Panov, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers SFB649DP2010-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    22. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    23. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.

    More about this item

    Keywords

    Heston model; vanilla option; stochastic volatility; Monte Carlo simulation; Feller condition; option pricing with FFT;

    JEL classification:

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

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