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On the valuation of fader and discrete barrier options in Heston's Stochastic Volatility Model

  • Griebsch, Susanne
  • Wystup, Uwe
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    We focus on closed-form option pricing in Hestons stochastic volatility model, in which closed-form formulas exist only for few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times.

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    Paper provided by Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF) in its series CPQF Working Paper Series with number 17.

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    Date of creation: 2008
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    Handle: RePEc:zbw:cpqfwp:17
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    1. Shephard, N.G., 1991. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory," Econometric Theory, Cambridge University Press, vol. 7(04), pages 519-529, December.
    2. Grunbichler, Andreas & Longstaff, Francis A., 1996. "Valuing futures and options on volatility," Journal of Banking & Finance, Elsevier, vol. 20(6), pages 985-1001, July.
    3. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
    4. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
    5. Kilin, Fiodar, 2007. "Accelerating the calibration of stochastic volatility models," CPQF Working Paper Series 6, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    6. Ansgar Belke & Thorsten Polleit, 2005. "(How) Do Stock Market Returns React to Monetary Policy? - An ARDL Cointegration Analysis for Germany," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 253/2005, Department of Economics, University of Hohenheim, Germany.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    8. Kilin, Fiodar, 2006. "Accelerating the calibration of stochastic volatility models," MPRA Paper 2975, University Library of Munich, Germany, revised 22 Apr 2007.
    9. Susanne Kruse & Ulrich Nögel, 2005. "On the pricing of forward starting options in Heston’s model on stochastic volatility," Finance and Stochastics, Springer, vol. 9(2), pages 233-250, 04.
    10. Ansgar Belke & Thorsten Polleit, 2006. "How the ECB and the US Fed Set Interest Rates," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 269/2006, Department of Economics, University of Hohenheim, Germany.
    11. Wollersheim, Jutta & Barthel, Erich, 2008. "Kulturunterschiede bei Mergers & Acquisitions: Entwicklung eines Konzeptes zur Durchführung einer Cultural Due Diligence," Frankfurt School - Working Paper Series 94, Frankfurt School of Finance and Management.
    12. Bannier, Christina E., 2007. "Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotation incidences?," Frankfurt School - Working Paper Series 83, Frankfurt School of Finance and Management.
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