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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
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    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.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697688.2010.503375
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 11 (2011)
    Issue (Month): 5 ()
    Pages: 693-709

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    Handle: RePEc:taf:quantf:v:11:y:2011:i:5:p:693-709

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    Related research

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

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    1. Christina Bannier, 2007. "Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotiation incidences?," Financial Markets and Portfolio Management, Springer, vol. 21(4), pages 445-470, December.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:
    1. 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.
    2. 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.
    3. Dietmar Harhoff & Elisabeth Mueller & John Van Reenen, 2013. "What are the Channels for Technology Sourcing? Panel Data Evidence from German Companies," CEP Discussion Papers dp1193, Centre for Economic Performance, LSE.
    4. 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.
    5. 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.
    6. 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.
    7. Susanne Griebsch, 2013. "The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques," Review of Derivatives Research, Springer, vol. 16(2), pages 135-165, July.
    8. 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.

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