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Unifying exotic option closed formulas

  • Esquível, Manuel L.
  • Veiga, Carlos
  • Wystup, Uwe
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    This paper aims to unify exotic option closed formulas by generalizing a large class of existing formulas and by setting a framework that allows for further generalizations. The formula presented covers options from the plain vanilla to most, if not all, mountain range exotic options and is developed in a multi-asset, multi-currency Black-Scholes model with time dependent parameters. The general formula not only covers existing cases but also enables the combination of diverse features from different types of exotic options. It also creates implicitly a language to describe payoffs that can be used in industrial applications to decouple the functions of payoff definition from pricing functions. Examples of several exotic options are presented, benchmarking the closed formulas' performance against Monte Carlo simulations. Results show a consistent over performance of the closed formula reducing calculation time by double digit factors.

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    File URL: http://econstor.eu/bitstream/10419/40174/1/634827219.pdf
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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 23.

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    Date of creation: 2010
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    Handle: RePEc:zbw:cpqfwp:23
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    1. 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.
    2. Ansgar Belke & Thorsten Polleit, 2007. "How the ECB and the US Fed set interest rates," Applied Economics, Taylor & Francis Journals, vol. 39(17), pages 2197-2209.
    3. Roßbach, Peter & Gießamer, Dirk, 2009. "Ein eLearning-System zur Unterstützung der Wissensvermittlung von Web-Entwicklern in Sicherheitsthemen," Frankfurt School - Working Paper Series 116, Frankfurt School of Finance and Management.
    4. Hankir, Yassin & Rauch, Christian & Umber, Marc P., 2009. "It's the market power, stupid! Stock return patterns in international bank M&A," Frankfurt School - Working Paper Series 129, Frankfurt School of Finance and Management.
    5. Roßbach, Peter, 2009. "Die Rolle des Internets als Informationsbeschaffungsmedium in Banken," Frankfurt School - Working Paper Series 120, Frankfurt School of Finance and Management.
    6. Bannier, Christina E., 2009. "Is there a hold-up benefit in heterogeneous multiple bank financing?," Frankfurt School - Working Paper Series 117, Frankfurt School of Finance and Management.
    7. Bannier, Christina E. & Hänsel, Dennis N., 2007. "Determinants of banks' engagement in loan securitization," Frankfurt School - Working Paper Series 85, Frankfurt School of Finance and Management.
    8. 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.
    9. Björk, Tomas & Landen, Camilla, 2000. "On the Term Structure of Futures and Forward Prices," SSE/EFI Working Paper Series in Economics and Finance 0417, Stockholm School of Economics, revised 20 Dec 2000.
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