IDEAS home Printed from https://ideas.repec.org/p/zbw/cpqfwp/23.html
   My bibliography  Save this paper

Unifying exotic option closed formulas

Author

Listed:
  • Esquível, Manuel L.
  • Veiga, Carlos
  • Wystup, Uwe

Abstract

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.

Suggested Citation

  • Esquível, Manuel L. & Veiga, Carlos & Wystup, Uwe, 2010. "Unifying exotic option closed formulas," CPQF Working Paper Series 23, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
  • Handle: RePEc:zbw:cpqfwp:23
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/40174/1/634827219.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Herrmann-Pillath, Carsten, 2009. "Kulturelle Hybridisierung und Wirtschaftstransformation in China," Frankfurt School - Working Paper Series 115, Frankfurt School of Finance and Management.
    2. Herrmann-Pillath, Carsten, 2008. "Neuroeconomics, naturalism and language," Frankfurt School - Working Paper Series 108, Frankfurt School of Finance and Management.
    3. C. Herrmann-Pillath, 2011. "A Neurolinguistic Approach to Performativity in Economics," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 2.
    4. Demidova-Menzel, Nadeshda & Heidorn, Thomas, 2007. "Gold in the investment portfolio," Frankfurt School - Working Paper Series 87, Frankfurt School of Finance and Management.
    5. P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
    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. Cremers, Heinz & Walzner, Jens, 2007. "Risikosteuerung mit Kreditderivaten unter besonderer Berücksichtigung von Credit Default Swaps," Frankfurt School - Working Paper Series 80, Frankfurt School of Finance and Management.
    8. Heidorn, Thomas & Kaiser, Dieter G. & Roder, Christoph, 2009. "Empirische Analyse der Drawdowns von Dach-Hedgefonds," Frankfurt School - Working Paper Series 109, Frankfurt School of Finance and Management.
    9. Herrmann-Pillath, Carsten, 2009. "Outline of a Darwinian theory of money," Frankfurt School - Working Paper Series 128, Frankfurt School of Finance and Management.
    10. 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.
    11. Almer, Thomas & Heidorn, Thomas & Schmaltz, Christian, 2008. "The dynamics of short- and long-term CDS-spreads of banks," Frankfurt School - Working Paper Series 95, Frankfurt School of Finance and Management.
    12. Schanz, Kay-Michael & Richard, Jörg & Schalast, Christoph, 2004. "Unternehmen im Prime Standard staying public oder going private? Nutzenanalyse der Börsennotiz," Frankfurt School - Working Paper Series 60, Frankfurt School of Finance and Management.
    13. Schalast, Christoph & Ockens, Klaas & Jobe, Clemens J. & Safran, Robert, 2006. "Work-out und Servicing von notleidenden Krediten: Berichte und Referate des HfB-NPL Servicing Forums 2006," Frankfurt School - Working Paper Series 76, Frankfurt School of Finance and Management.
    14. Hirsch, Christian & Bannier, Christina E., 2007. "The economics of rating watchlists: Evidence from rating changes," CFS Working Paper Series 2008/02, Center for Financial Studies (CFS).
    15. Heidorn, Thomas & Siragusano, Tindaro, 2004. "Die Anwendbarkeit der Behavioral Finance im Devisenmarkt," Frankfurt School - Working Paper Series 52, Frankfurt School of Finance and Management.
    16. Demidova-Menzel, Nadeshda & Heidorn, Thomas, 2007. "Commodities in asset management," Frankfurt School - Working Paper Series 81, Frankfurt School of Finance and Management.
    17. Cremers, Heinz & Walzner, Jens, 2009. "Modellierung des Kreditrisikos im Portfoliofall," Frankfurt School - Working Paper Series 127, Frankfurt School of Finance and Management.
    18. Conze, Antoine & Viswanathan, 1991. "Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-1907, December.
    19. Schäffler, Christian & Schmaltz, Christian, 2009. "Market liquidity: an introduction for practitioners," Frankfurt School - Working Paper Series 131, Frankfurt School of Finance and Management.
    20. Schalast, Christoph, 2008. "Der deutsche NPL-Markt 2007: aktuelle Entwicklungen, Verkauf und Bewertung ; Berichte und Referate des NPL-Forums 2007," Frankfurt School - Working Paper Series 90, Frankfurt School of Finance and Management.
    21. Schalast, Christoph & Stralkowski, Ingo, 2008. "10 Jahre deutsche Buyouts," Frankfurt School - Working Paper Series 89, Frankfurt School of Finance and Management.
    22. Bannier, Christina E. & Grote, Michael H., 2008. "Equity gap? - Which equity gap? On the financing structure of Germany's Mittelstand," Frankfurt School - Working Paper Series 106, Frankfurt School of Finance and Management.
    23. Herrmann-Pillath, Carsten, 2008. "The naturalistic turn in economics: implications for the theory of finance," Frankfurt School - Working Paper Series 105, Frankfurt School of Finance and Management.
    24. Polleit, Thorsten & Gerdesmeier, Dieter, 2005. "Measures of excess liquidity," Frankfurt School - Working Paper Series 65, Frankfurt School of Finance and Management.
    25. Cremers, Heinz & Walzner, Jens, 2009. "Modellierung des Kreditrisikos im Einwertpapierfall," Frankfurt School - Working Paper Series 126, Frankfurt School of Finance and Management.
    26. Christina E. Bannier & Patrick Behr & Andre Güttler, 2010. "Rating opaque borrowers: why are unsolicited ratings lower?," Review of Finance, European Finance Association, vol. 14(2), pages 263-294.
    27. Löchel, Horst & Baumann, Stefan, 2006. "The endogeneity approach of the theory of optimum currency areas: what does it mean for ASEAN + 3?," Frankfurt School - Working Paper Series 70, Frankfurt School of Finance and Management.
    28. 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.
    29. Bannier, Christina E. & Hirsch, Christian W., 2010. "The economic function of credit rating agencies - What does the watchlist tell us?," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3037-3049, December.
    30. Polleit, Thorsten, 2004. "The slowdown in German bank lending - revisited," Frankfurt School - Working Paper Series 53, Frankfurt School of Finance and Management.
    31. Löhr, Andreas & Cremers, Heinz, 2007. "Deskription und Bewertung strukturierter Produkte unter besonderer Berücksichtigung verschiedener Marktszenarien," Frankfurt School - Working Paper Series 82, Frankfurt School of Finance and Management.
    32. Heidorn, Thomas & Gerhold, Mirko, 2004. "Investitionen und Emissionen von Convertible Bonds (Wandelanleihen)," Frankfurt School - Working Paper Series 50, Frankfurt School of Finance and Management.
    33. Christina E. Bannier, 2010. "Is there a Holdup Benefit in Heterogeneous Multiple Bank Financing?," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 166(4), pages 641-661, December.
    34. 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.
    35. Werner, Karl & Moormann, Jürgen, 2009. "Efficiency and profitability of European banks: how important is operational efficiency?," Frankfurt School - Working Paper Series 111, Frankfurt School of Finance and Management.
    36. 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.
    37. Christina Bannier, 2007. "Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotiation incidences?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 21(4), pages 445-470, December.
    38. Alram, Johannes, 2009. "Konstruktion einer Anleihe mit hypothekarischer Besicherung," Frankfurt School - Working Paper Series 113, Frankfurt School of Finance and Management.
    39. Heimer, Thomas & Arend, Sebastian, 2008. "The genesis of the Black-Scholes option pricing formula," Frankfurt School - Working Paper Series 98, Frankfurt School of Finance and Management.
    40. Heidorn, Thomas & Pleißner, Mathias, 2008. "Determinanten europäischer CMBS spreads: ein empirisches Modell zur Bestimmung der Risikoaufschläge von commercial mortgage-backed securities (CMBS)," Frankfurt School - Working Paper Series 101, Frankfurt School of Finance and Management.
    41. Schalast, Christoph & Bolder, Markus & Radünz, Claus & Siepmann, Stephanie & Weber, Thorsten, 2009. "Transaktionen und Servicing in der Finanzkrise: Berichte und Referate des Frankfurt School NPL Forums 2008," Frankfurt School - Working Paper Series 112, Frankfurt School of Finance and Management.
    42. Gerdesmeier, Dieter & Roffia, Barbara, 2007. "Monetary analysis: a VAR perspective," Frankfurt School - Working Paper Series 78, Frankfurt School of Finance and Management.
    43. Roßbach, Peter, 2009. "Die Rolle des Internets als Informationsbeschaffungsmedium in Banken," Frankfurt School - Working Paper Series 120, Frankfurt School of Finance and Management.
    44. 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.
    45. Dickler, Robert A. & Schalast, Christoph, 2006. "Distressed debt in Germany: What's next? Possible innovative exit strategies," Frankfurt School - Working Paper Series 73, Frankfurt School of Finance and Management.
    46. Becker, Gernot M. & Seeger, Norbert, 2003. "Internationale Cash Flow-Rechnungen aus Eigner- und Gläubigersicht," Frankfurt School - Working Paper Series 48, Frankfurt School of Finance and Management.
    47. Heun, Michael & Schlink, Torsten, 2004. "Early warning systems of financial crises: implementation of a currency crisis model for Uganda," Frankfurt School - Working Paper Series 59, Frankfurt School of Finance and Management.
    48. Löchel, Horst & Polleit, Thorsten, 2005. "A case for money in the ECB monetary policy strategy," Frankfurt School - Working Paper Series 61, Frankfurt School of Finance and Management.
    49. Chevalier, Pierre & Heidorn, Thomas & Krieger, Christian, 2003. "Temperaturderivate zur strategischen Absicherung von Beschaffungs- und Absatzrisiken," Frankfurt School - Working Paper Series 49, Frankfurt School of Finance and Management.
    50. Vetter, Michael & Cremers, Heinz, 2008. "Das IRB-Modell des Kreditrisikos im Vergleich zum Modell einer logarithmisch normalverteilten Verlustfunktion," Frankfurt School - Working Paper Series 102, Frankfurt School of Finance and Management.
    51. 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.
    52. Heimer, Thomas & Hölscher, Luise & Werner, Matthias Ralf, 2008. "Access to finance and venture capital for industrial SMEs," Frankfurt School - Working Paper Series 97, Frankfurt School of Finance and Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Yu, Xiaofan, 2011. "A spatial interpretation of the persistency of China's provincial inequality," Frankfurt School - Working Paper Series 171, Frankfurt School of Finance and Management.
    3. Böing, Philipp & Müller, Elisabeth, 2012. "Technological Capabilities of Chinese Enterprises: Who is Going to Compete Abroad?," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62081, Verein für Socialpolitik / German Economic Association.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Detering, Nils & Weber, Andreas & Wystup, Uwe, 2010. "Return distributions of equity-linked retirement plans," CPQF Working Paper Series 27, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    2. Veiga, Carlos & Wystup, Uwe, 2010. "Ratings of structured products and issuers' commitments," CPQF Working Paper Series 26, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    3. Scholz, Peter & Walther, Ursula, 2010. "Investment certificates under German taxation: Benefit or burden for structured products' performance?," CPQF Working Paper Series 24, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    4. Natalie Packham & Lutz Schloegl & Wolfgang M. Schmidt, 2013. "Credit gap risk in a first passage time model with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1871-1889, December.
    5. Beyna, Ingo & Wystup, Uwe, 2011. "Characteristic functions in the Cheyette Interest Rate Model," CPQF Working Paper Series 28, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    6. Packham, Natalie & Schlögl, Lutz & Schmidt, Wolfgang M., 2009. "Credit dynamics in a first passage time model with jumps," CPQF Working Paper Series 21, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    7. Herrmann-Pillath, Carsten, 2011. "The evolutionary approach to entropy: Reconciling Georgescu-Roegen's natural philosophy with the maximum entropy framework," Ecological Economics, Elsevier, vol. 70(4), pages 606-616, February.
    8. Herrmann-Pillath, Carsten, 2010. "Meaning and function in the theory of consumer choice: dual selves in evolving networks," Frankfurt School - Working Paper Series 153, Frankfurt School of Finance and Management.
    9. Beyna, Ingo & Wystup, Uwe, 2010. "On the calibration of the Cheyette interest rate model," CPQF Working Paper Series 25, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    10. Heidorn, Thomas & Kahlert, Dennis, 2010. "Implied correlations of iTraxx tranches during the financial crisis," Frankfurt School - Working Paper Series 145, Frankfurt School of Finance and Management.
    11. Boeing, Philipp & Sandner, Philipp, 2011. "The innovative performance of China's national innovation system," Frankfurt School - Working Paper Series 158, Frankfurt School of Finance and Management.
    12. Kostka, Genia & Zhou, Jianghua, 2010. "Chinese firms entering China's low-income market: Gaining competitive advantage by partnering governments," Frankfurt School - Working Paper Series 147, Frankfurt School of Finance and Management.
    13. Herrmann-Pillath, Carsten, 2010. "Rethinking evolution, entropy and economics: A triadic conceptual framework for the maximum entropy principle as applied to the growth of knowledge," Frankfurt School - Working Paper Series 146, Frankfurt School of Finance and Management.
    14. Roßbach, Peter & Karlow, Denis, 2011. "The stability of traditional measures of index tracking quality," Frankfurt School - Working Paper Series 164, Frankfurt School of Finance and Management.
    15. Kostka, Genia & Shin, Kyoung, 2011. "Energy service companies in China: The role of social networks and trust," Frankfurt School - Working Paper Series 168, Frankfurt School of Finance and Management.
    16. Dietmar Harhoff & Elisabeth Mueller & John Van 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.
    17. Carsten Herrmann-Pillath, 2012. "Making Sense of Institutional Change in China: The Cultural Dimension of Economic Growth and Modernization," International Economic Association Series, in: Masahiko Aoki & Timur Kuran & Gérard Roland (ed.), Institutions and Comparative Economic Development, chapter 13, pages 254-278, Palgrave Macmillan.
    18. Klein, Michael, 2012. "Infrastructure policy: Basic design options," Frankfurt School - Working Paper Series 185, Frankfurt School of Finance and Management.
    19. Klein, Michael, 2011. "Enrichment with growth," Frankfurt School - Working Paper Series 172, Frankfurt School of Finance and Management.
    20. Carsten Herrmann-Pillath, 2013. "Performativity of economic systems: approach and implications for taxonomy," Journal of Economic Methodology, Taylor & Francis Journals, vol. 20(2), pages 139-163, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:cpqfwp:23. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/hfbfide.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.