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Valuing options in Heston's stochastic volatility model: Another analytical approach

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  • Frontczak, Robert

Abstract

We are concerned with the valuation of European options in Heston's stochastic volatility model with correlation. Based on Mellin transforms we present new closed-form solutions for the price of European options and hedging parameters. In contrast to Fourier-based approaches where the transformation variable is usually the log-stock price at maturity, our framework focuses on transforming the current stock price. Our solution has the nice feature that similar to the approach of Carr and Madan (1999) it requires only a single integration. We make numerical tests to compare our results to Heston's solution based on Fourier inversion and investigate the accuracy of the derived pricing formulae.

Suggested Citation

  • Frontczak, Robert, 2009. "Valuing options in Heston's stochastic volatility model: Another analytical approach," Tübinger Diskussionsbeiträge 326, University of Tübingen, School of Business and Economics.
    • Handle: RePEc:zbw:tuedps:326
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    as
    1. Kleinert, Jörn & Toubal, Farid, 2007. "The impact of locating production abroad on activities at home," Tübinger Diskussionsbeiträge 314, University of Tübingen, School of Business and Economics.
    2. Claudia M. Buch & Jörn Kleinert, 2008. "Exchange Rates and FDI: Goods versus Capital Market Frictions," The World Economy, Wiley Blackwell, vol. 31(9), pages 1185-1207, September.
    3. Dymke, Björn M. & Walter, Andreas, 2006. "Insider trading in Germany: Do corporate insiders exploit inside information?," Tübinger Diskussionsbeiträge 309, University of Tübingen, School of Business and Economics.
    4. Jörn Kleinert & Farid Toubal, 2010. "Gravity for FDI," Review of International Economics, Wiley Blackwell, vol. 18(1), pages 1-13, February.
    5. Laszlo Goerke & Markus Pannenberg, 2007. "Trade Union Membership and Works Councils in West Germany," Industrielle Beziehungen - Zeitschrift fuer Arbeit, Organisation und Management - The German Journal of Industrial Relations, Rainer Hampp Verlag, vol. 14(2), pages 154-175.
    6. Schnabl, Gunther, 2003. "China: a stabilizing or deflationary influence in East Asia?The problem of conflicted virtue," Tübinger Diskussionsbeiträge 263, University of Tübingen, School of Business and Economics.
    7. Hager, Svenja & Schöbel, Rainer, 2006. "Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms," Tübinger Diskussionsbeiträge 300, University of Tübingen, School of Business and Economics.
    8. Ronald McKinnon & Gunther Schnabl, 2006. "The East Asian Dollar Standard, Fear of Floating, and Original Sin," Chapters, in: Volbert Alexander & Hans-Helmut Kotz (ed.), Global Divergence in Trade, Money and Policy, chapter 3, pages 45-71, Edward Elgar Publishing.
    9. Zaby, Alexandra K., 2009. "The propensity to patent in oligopolistic markets," Tübinger Diskussionsbeiträge 323, University of Tübingen, School of Business and Economics.
    10. Felbermayr, Gabriel J. & Toubal, Farid, 2010. "Cultural proximity and trade," European Economic Review, Elsevier, vol. 54(2), pages 279-293, February.
    11. Gunther Schnabl, 2004. "De jure versus de facto Exchange Rate Stabilization in Central and Eastern Europe," Aussenwirtschaft, University of St. Gallen, School of Economics and Political Science, Swiss Institute for International Economics and Applied Economics Research, vol. 59(02), pages 171-190, June.
    12. Pitterle, Ingo & Steffen, Dirk, 2004. "Welfare Effects of Fiscal Policy under Alternative Exchange Rate Regimes : The Role of the Scale Variable of Money Demand," Tübinger Diskussionsbeiträge 284, University of Tübingen, School of Business and Economics.
    13. Schanz, Sebastian, 2004. "Die Auswirkung alternativer Gewinnverwendung von Kapitalgesellschaften - im Rahmen des Halbeinkünfteverfahrens - auf die Vermögenspositionen Residualanspruchsberechtigter," Tübinger Diskussionsbeiträge 279, University of Tübingen, School of Business and Economics.
    14. Rostek, Stefan & Schöbel, Rainer, 2006. "Risk preference based option pricing in a fractional Brownian market," Tübinger Diskussionsbeiträge 299, University of Tübingen, School of Business and Economics.
    15. Grupp, Hariolf & Stadler, Manfred, 2004. "Technological Progress and Market Growth : An Empirical Study Based on the Quality-Ladder Approach," Tübinger Diskussionsbeiträge 281, University of Tübingen, School of Business and Economics.
    16. Heger, Diana & Zaby, Alexandra K., 2009. "The propensity to patent with vertically differentiated products: An empirical investigation," Tübinger Diskussionsbeiträge 325, University of Tübingen, School of Business and Economics.
    17. Hager, Svenja & Schöbel, Rainer, 2005. "A note on the correlation smile," Tübinger Diskussionsbeiträge 297, University of Tübingen, School of Business and Economics.
    18. Licht, Georg & Stadler, Manfred, 2003. "Auswirkungen öffentlicher Forschungsförderung auf die private F&E-Tätigkeit: Eine mikroökonomische Evaluation," Tübinger Diskussionsbeiträge 256, University of Tübingen, School of Business and Economics.
    19. Kleinert, Jörn & Toubal, Farid, 2005. "A Structural Model of Export versus Affiliates Production," Tübinger Diskussionsbeiträge 288, University of Tübingen, School of Business and Economics.
    20. Gunther Schnabl & Paul De Grauwe, 2004. "Nominal versus Real Convergence with Respect to EMU Accession - EMU Entry Scenarios for the New Member States," International Finance 0403008, University Library of Munich, Germany, revised 16 Feb 2005.
    21. Gabriel Felbermayr & Benjamin Jung, 2011. "Trade Intermediation and the Organization of Exporters," Review of International Economics, Wiley Blackwell, vol. 19(4), pages 634-648, September.
    22. Gabriel Felbermayr & Benjamin Jung, 2011. "Sorting It Out: Technical Barriers to Trade and Industry Productivity," Open Economies Review, Springer, vol. 22(1), pages 93-117, February.
    23. J.Baten & J.Wallusch, 2005. "Market Integration and Disintegration of Poland and Germany in the 18th Century," Economies et Sociétés (Serie 'Histoire Economique Quantitative'), Association Française de Cliométrie (AFC), issue 33, pages 1233-1264, July.
    24. Gabriel Felbermayr & Benjamin Jung, 2011. "Trade Intermediation and the Organization of Exporters," Review of International Economics, Wiley Blackwell, vol. 19(4), pages 634-648, September.
    25. Lachmund, Andreas & Kiesewetter, Dirk, 2004. "Wirkungen einer Abgeltungssteuer auf Investitionsentscheidungen und Kapitalstruktur von Unternehmen," Tübinger Diskussionsbeiträge 278, University of Tübingen, School of Business and Economics.
    26. repec:ebl:ecbull:v:4:y:2005:i:12:p:1-7 is not listed on IDEAS
    27. Güth, Werner & Stadler, Manfred, 2004. "Path Dependence Without Denying Deliberation : An Exercise Model Connecting Rationality and Evolution," Tübinger Diskussionsbeiträge 282, University of Tübingen, School of Business and Economics.
    28. Roos, Melanie & Hümmer, Carolin, 2009. "Die Akzeptanz von Corporate Social Responsibility in Deutschland," Tübinger Diskussionsbeiträge 321, University of Tübingen, School of Business and Economics.
    29. Baur, Dirk & Schulze, Niels, 2005. "Coexceedances in financial markets--a quantile regression analysis of contagion," Emerging Markets Review, Elsevier, vol. 6(1), pages 21-43, April.
    30. Stadler, Manfred, 2006. "Education and innovation as twin-engines of growth," Tübinger Diskussionsbeiträge 302, University of Tübingen, School of Business and Economics.
    31. Yu, Peiyi & Neus, Werner, 2005. "Market Structure, Scale Efficiency, and Risk as Determinants of German Banking Profitability," Tübinger Diskussionsbeiträge 294, University of Tübingen, School of Business and Economics.
    32. Schüle, Tobias, 2006. "Creditor coordination with social learning and endogenous timing of credit decisions," Tübinger Diskussionsbeiträge 307, University of Tübingen, School of Business and Economics.
    33. Jung, Robert & Kukuk, Martin & Liesenfeld, Roman, 2005. "Time Series of Count Data: Modelling and Estimation," Economics Working Papers 2005-08, Christian-Albrechts-University of Kiel, Department of Economics.
    34. Heger, Diana & Zaby, Alexandra K., 2009. "The propensity to patent with horizontally differentiated products: An empirical investigation," Tübinger Diskussionsbeiträge 324, University of Tübingen, School of Business and Economics.
    35. Neubecker, Leslie & Stadler, Manfred, 2003. "In hunt for size: Merger formation in the oil industry," Tübinger Diskussionsbeiträge 258, University of Tübingen, School of Business and Economics.
    36. Schüle, Tobias, 2006. "Forbearance lending and soft budget constraints in a model of multiple heterogeneous bank financing," Tübinger Diskussionsbeiträge 303, University of Tübingen, School of Business and Economics.
    37. Koepke, Nikola & Baten, Joerg, 2005. "The biological standard of living in Europe during the last two millennia," European Review of Economic History, Cambridge University Press, vol. 9(1), pages 61-95, April.
    38. Zaby, Alexandra K., 2005. "Losing the lead: Patents and the disclosure requirement," Tübinger Diskussionsbeiträge 296, University of Tübingen, School of Business and Economics.
    39. Thaut, Michael, 2003. "Die individuelle Vorteilhaftigkeit der privaten Rentenversicherung: Steuervorteile, Lebenserwartung und Stornorisiken," Tübinger Diskussionsbeiträge 264, University of Tübingen, School of Business and Economics.
    40. Maier, Ramona & Merz, Michael, 2008. "Credibility theory and filter theory in discrete and continuous time," Tübinger Diskussionsbeiträge 318, University of Tübingen, School of Business and Economics.
    41. Schnabl, Gunther, 2005. "Der Festkurs als merkantilistische Handelspolitik : Chinas Währungs- und Geldpolitik im Umfeld globaler Ungleichgewichte," Tübinger Diskussionsbeiträge 291, University of Tübingen, School of Business and Economics.
    42. Stadler, Manfred, 2004. "Bildung, Innovationsdynamik und Produktivitätswachstum," Tübinger Diskussionsbeiträge 280, University of Tübingen, School of Business and Economics.
    43. Lengsfeld, Stephan & Schiller, Ulf, 2003. "Transfer Pricing Based on Actual versus Standard Costs," Tübinger Diskussionsbeiträge 272, University of Tübingen, School of Business and Economics.
    44. Bayer, Stefan, 2003. "Possibilities and limitations of economically valuating ecological damages," Tübinger Diskussionsbeiträge 254, University of Tübingen, School of Business and Economics.
    45. Godart, Olivier N. & Toubal, Farid, 2005. "Cross The Border and Close The Gap? : How Do Migrants Enhance Trade," Tübinger Diskussionsbeiträge 289, University of Tübingen, School of Business and Economics.
    46. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    47. Frontczak, Robert & Schöbel, Rainer, 2009. "On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options," Tübinger Diskussionsbeiträge 320, University of Tübingen, School of Business and Economics.
    48. Molzahn, Alexander, 2004. "Optimale Fiskalpolitik und endogenes Wachstum," Tübinger Diskussionsbeiträge 285, University of Tübingen, School of Business and Economics.
    49. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    50. Frontczak, Robert & Schöbel, Rainer, 2008. "Pricing American options with Mellin transforms," Tübinger Diskussionsbeiträge 319, University of Tübingen, School of Business and Economics.
    51. Klein, Nicole, 2009. "Die Balanced Scorecard als Basis einer Customer Care Scorecard zur Konzeption einer systematischen Kundenpflege," Tübinger Diskussionsbeiträge 322, University of Tübingen, School of Business and Economics.
    52. Töpfer, Klaus, 2006. "Offene Fragen und wissenschaftliche Herausforderungen der Entwicklungsund Umweltpolitik," Tübinger Diskussionsbeiträge 301, University of Tübingen, School of Business and Economics.
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    Cited by:

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    More about this item

    Keywords

    Stochastic volatility; European option; Mellin transform;
    All these keywords.

    JEL classification:

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

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