Advanced Search
MyIDEAS: Login to save this paper or follow this series

Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility

Contents:

Author Info

  • Frey, Rüdiger
Registered author(s):

    Abstract

    In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of erivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes model; they have been developed in an effort to build models that are flexible enough to cope with the known deficits of the classical Black-Scholes model. We start by briefly recalling the standard theory for pricing and hedging derivatives in complete frictionless markets and the classical Black-Scholes model. After a review of the known empirical contradictions to the classical Black-Scholes model we consider models with level-dependent volatility. Most of this survey is devoted to derivative asset analysis in stochastic volatility models. We discuss several recent developments in the theory of derivative pricing under incompleteness in the context of stochastic volatility models and review analytical and numerical approaches to the actual computation of option values.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb401.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 401.

    as in new window
    Length: pages
    Date of creation: Jan 1997
    Date of revision:
    Handle: RePEc:bon:bonsfb:401

    Contact details of provider:
    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: option pricing; Black-Scholes model; stochastic volatility; incomplete markets;

    Find related papers by JEL classification:

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
    2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    3. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
    4. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9613, Universite de Montreal, Departement de sciences economiques.
    5. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 5(1), pages 13-32.
    6. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    7. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers, University of California at Berkeley RPF-232, University of California at Berkeley.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    9. Paul Embrechts, 1996. "Actuarial versus Financial Pricing of Insurance," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 96-17, Wharton School Center for Financial Institutions, University of Pennsylvania.
    10. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
    11. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 2(2), pages 63-86.
    12. Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 29(02), pages 241-261, June.
    13. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B, University of Bonn, Germany 209, University of Bonn, Germany.
    14. E. Platen & M. Schweizer, 1997. "On Feedback Effects from Hedging Derivatives," SFB 373 Discussion Papers 1997,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B, University of Bonn, Germany 294, University of Bonn, Germany.
    16. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
    17. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 36, pages 394.
    18. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, American Finance Association, vol. 49(3), pages 771-818, July.
    19. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
    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 in new window

    Cited by:
    1. David Heath & S. Hurst & Eckhard Platen, 1999. "Modelling the Stochastic Dynamics of Volatility for Equity Indices," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 7, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2003. "A Comparison of q-optimal Option Prices in a Stochastic Volatility Model with Correlation," OFRC Working Papers Series, Oxford Financial Research Centre 2003mf02, Oxford Financial Research Centre.
    3. Rüdiger Frey & Carlos A. Sin, 1999. "Bounds on European Option Prices under Stochastic Volatility," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(2), pages 97-116.
    4. Alexander, Carol & Nogueira, Leonardo M., 2007. "Model-free hedge ratios and scale-invariant models," Journal of Banking & Finance, Elsevier, Elsevier, vol. 31(6), pages 1839-1861, June.
    5. Carol Alexander & Alexander Rubinov & Markus Kalepky & Stamatis Leontsinis, 2010. "Regime-Dependent Smile-Adjusted Delta Hedging," ICMA Centre Discussion Papers in Finance, Henley Business School, Reading University icma-dp2010-10, Henley Business School, Reading University.
    6. Vicky Henderson, 2002. "Analytical Comparisons of Option prices in Stochastic Volatility Models," OFRC Working Papers Series, Oxford Financial Research Centre 2002mf03, Oxford Financial Research Centre.
    7. Eckhard Platen & Renata Rendek, 2010. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 282, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Maxim Bichuch & Stephan Sturm, 2011. "Portfolio Optimization under Convex Incentive Schemes," Papers 1109.2945, arXiv.org, revised Oct 2013.
    9. Wei Chen, 2013. "G-consistent price system and bid-ask pricing for European contingent claims under Knightian uncertainty," Papers 1308.6256, arXiv.org, revised Sep 2013.
    10. Kazmerchuk, Yuriy & Swishchuk, Anatoliy & Wu, Jianhong, 2007. "The pricing of options for securities markets with delayed response," Mathematics and Computers in Simulation (MATCOM), Elsevier, Elsevier, vol. 75(3), pages 69-79.
    11. Vicky Henderson & David Hobson, 2001. "Passport options with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(2), pages 97-118.
    12. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, Springer, vol. 10(2), pages 222-249, April.
    13. Schoeneborn, Torsten & Schied, Alexander, 2007. "Liquidation in the Face of Adversity: Stealth Vs. Sunshine Trading, Predatory Trading Vs. Liquidity Provision," MPRA Paper 5548, University Library of Munich, Germany.
    14. Vicky Henderson & David Hobson & Sam Howison & Tino Kluge, 2005. "A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation," Review of Derivatives Research, Springer, Springer, vol. 8(1), pages 5-25, June.
    15. Christodoulakis, George A. & Satchell, Stephen E., 1999. "The simulation of option prices with application to LIFFE options on futures," European Journal of Operational Research, Elsevier, Elsevier, vol. 114(2), pages 249-262, April.
    16. Carol Alexander & Leonardo M. Nogueira, 2006. "Hedging Options with Scale-Invariant Models," ICMA Centre Discussion Papers in Finance, Henley Business School, Reading University icma-dp2006-03, Henley Business School, Reading University.
    17. Wolfgang Hardle & Torsten Kleinow & Alexander Korostelev & Camille Logeay & Eckhard Platen, 2001. "Semiparametric Diffusion Estimation and Application to a Stock Market Model," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 51, Quantitative Finance Research Centre, University of Technology, Sydney.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:bon:bonsfb:401. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (BGSE Office).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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