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On the valuation of fader and discrete barrier options in Heston's stochastic volatility model

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  • Susanne Griebsch
  • Uwe Wystup

Abstract

We focus on closed-form option pricing in Heston's stochastic volatility model, where closed-form formulas exist only for a few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this closed-form 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 the computational accuracy.

Suggested Citation

  • Susanne Griebsch & Uwe Wystup, 2011. "On the valuation of fader and discrete barrier options in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 693-709.
  • Handle: RePEc:taf:quantf:v:11:y:2011:i:5:p:693-709 DOI: 10.1080/14697688.2010.503375
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    Cited by:

    1. Inklaar, Robert & Koetter, Michael & Noth, Felix, 2012. "Who's afraid of big bad banks? Bank competition, SME, and industry growth," Frankfurt School - Working Paper Series 197, Frankfurt School of Finance and Management.
    2. Dietmar Harhoff & Elisabeth Mueller & John Reenen, 2014. "What are the Channels for Technology Sourcing? Panel Data Evidence from German Companies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(1), pages 204-224, March.
    3. Kostka, Genia & Moslener, Ulf & Andreas, Jan G., 2011. "Barriers to energy efficiency improvement: Empirical evidence from small-and-medium sized enterprises in China," Frankfurt School - Working Paper Series 178, Frankfurt School of Finance and Management.
    4. Libman, Alexander & Kozlov, Vladimir & Schultz, André, 2012. "Roving bandits in action: Outside option and governmental predation in autocracies," Frankfurt School - Working Paper Series 190, Frankfurt School of Finance and Management.
    5. Boeing, Philipp & Mueller, Elisabeth & Sandner, Philipp, 2012. "What makes Chinese firms productive? Learning from indigenous and foreign sources of knowledge," Frankfurt School - Working Paper Series 196, Frankfurt School of Finance and Management.
    6. Alexander Libman & Vladimir Kozlov & André Schultz, 2012. "Roving Bandits in Action: Outside Option and Governmental Predation in Autocracies," Kyklos, Wiley Blackwell, vol. 65(4), pages 526-562, November.
    7. Akira Yamazaki, 2016. "Generalized Barndorff-Nielsen And Shephard Model And Discretely Monitored Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-34, June.
    8. Böing, Philipp & Müller, Elisabeth, 2012. "Technological Capabilities of Chinese Enterprises: Who is Going to Compete Abroad?," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62081, Verein für Socialpolitik / German Economic Association.
    9. Susanne Griebsch, 2013. "The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques," Review of Derivatives Research, Springer, pages 135-165.
    10. Susanne Griebsch & Kay Pilz, 2012. "A Stochastic Approach to the Valuation of Barrier Options in Heston's Stochastic Volatility Model," Research Paper Series 309, Quantitative Finance Research Centre, University of Technology, Sydney.

    More about this item

    Keywords

    Exotic options; Heston model; Characteristic function; Multidimensional FFT;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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