IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

FX Smile in the Heston Model

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

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_10_02.pdf
File Function: Original version, 2010
Download Restriction: no

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/10/02.

as
in new window

Length: 33 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:wuu:wpaper:hsc1002
Contact details of provider: Postal: Wybrzeze Wyspianskiego 27, 50-370 Wroclaw
Phone: +48-71-3203530
Fax: +48-71-3202654
Web page: http://prac.im.pwr.wroc.pl/~hugo
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Mengmeng Guo & Wolfgang Karl Härdle, 2010. "Adaptive Interest Rate Modelling," SFB 649 Discussion Papers SFB649DP2010-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Raffaele Fiocco, 2010. "The optimal industry structure in a vertically related market," SFB 649 Discussion Papers SFB649DP2010-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers SFB649DP2010-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
  5. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
  6. Janek, Agnieszka & Kluge, Tino & Weron, Rafal & Wystup, Uwe, 2010. "FX Smile in the Heston Model," MPRA Paper 25491, University Library of Munich, Germany.
  7. Ulrich Horst & Traian A. Pirvu & Gonçalo Dos Reis, 2010. "On Securitization, Market Completion and Equilibrium Risk Transfer," SFB 649 Discussion Papers SFB649DP2010-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 443-453.
  9. Hautsch, Nikolaus & Hess, Dieter E. & Veredas, David, 2011. "The impact of macroeconomic news on quote adjustments, noise, and informational volatility," CFR Working Papers 11-06, University of Cologne, Centre for Financial Research (CFR).
  10. Wolfgang Karl Härdle & Yarema Okhrin & Weining Wang, 2010. "Uniform confidence bands for pricing kernels," SFB 649 Discussion Papers SFB649DP2010-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Michael C. Burda & Mark Weder, 2010. "Payroll Taxes, Social Insurance and Business Cycles," School of Economics Working Papers 2010-17, University of Adelaide, School of Economics.
  12. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  13. Sandra Schmidt & Dieter Nautz, 2010. "Why Do Financial Market Experts Misperceive Future Monetary Policy Decisions?," SFB 649 Discussion Papers SFB649DP2010-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  14. Ulrich Horst & Felix Naujokat, 2010. "Illiquidity and Derivative Valuation," SFB 649 Discussion Papers SFB649DP2010-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  15. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
  16. Hautsch, Nikolaus & Podolskij, Mark, 2010. "Pre-averaging based estimation of quadratic variation in the presence of noise and jumps: Theory, implementation, and empirical evidence," CFS Working Paper Series 2010/17, Center for Financial Studies (CFS).
  17. Basteck, Christian & Daniëls, Tijmen R. & Heinemann, Frank, 2013. "Characterising equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2620-2637.
  18. Wolfgang Karl Härdle & Rainer Schulz & Weining Wang, 2010. "Prognose mit nichtparametrischen Verfahren," SFB 649 Discussion Papers SFB649DP2010-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  19. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3774-3792.
  20. Puriya Abbassi & Dieter Nautz, 2010. "Monetary Transmission Right from the Start: The (Dis)Connection Between the Money Market and the ECB’s Main Refinancing Rates," Working Papers 1011, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 15 Jul 2010.
  21. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
  22. Vladimir Panov, 2010. "Non-Gaussian Component Analysis: New Ideas, New Proofs, New Applications," SFB 649 Discussion Papers SFB649DP2010-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  23. Adrian A. Dragulescu & Victor M. Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Papers cond-mat/0203046, arXiv.org, revised Nov 2002.
  24. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  25. A. Dragulescu & V. M. Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Computing in Economics and Finance 2002 127, Society for Computational Economics.
  26. Ulrich Horst & Santiago Moreno-Bromberg, 2011. "Efficiency and Equilibria in Games of Optimal Derivative Design," Papers 1107.0839, arXiv.org.
  27. Szymon Borak & Kai Detlefsen & Wolfgang Härdle, 2005. "FFT Based Option Pricing," SFB 649 Discussion Papers SFB649DP2005-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  28. Fengler, Matthias R. & Härdle, Wolfgang & Mammen, Enno, 2003. "Implied volatility string dynamics," SFB 373 Discussion Papers 2003,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  29. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
  30. Maria Grith & Wolfgang Karl Härdle & Melanie Schienle, 2010. "Nonparametric Estimation of Risk-Neutral Densities," SFB 649 Discussion Papers SFB649DP2010-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  31. Wolfgang Karl Härdle & Yuichi Mori & Jürgen Symanzik, 2012. "Computational Statistics (Journal)," SFB 649 Discussion Papers SFB649DP2012-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  32. Fang Yao, 2010. "Aggregate Hazard Function in Price-Setting: A Bayesian Analysis Using Macro Data," SFB 649 Discussion Papers SFB649DP2010-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  33. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  34. Thomas Post & Katja Hanewald, 2010. "Stochastic Mortality, Subjective Survival Expectations, and Individual Saving Behavior," SFB 649 Discussion Papers SFB649DP2010-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  35. Juliane Scheffel, 2010. "Honey, I’ll Be Working Late Tonight. The Effect of Individual Work Routines on Leisure Time Synchronization of Couples," SFB 649 Discussion Papers SFB649DP2010-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  36. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  37. Tompkins, Robert G. & D'Ecclesia, Rita L., 2006. "Unconditional return disturbances: A non-parametric simulation approach," Journal of Banking & Finance, Elsevier, vol. 30(1), pages 287-314, January.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:wuu:wpaper:hsc1002. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Rafal Weron)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.