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

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Author Info
Frey, Rüdiger
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.

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

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Date of creation: Jan 1997
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Handle: RePEc:bon:bonsfb:401

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
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Web page: http://www.bgse.uni-bonn.de/index.php?id=517

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

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

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.:
  1. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July. [Downloadable!] (restricted)
  2. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  3. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  4. E. Platen & M. Schweizer, . "On Feedback Effects from Hedging Derivatives," Sonderforschungsbereich 373 1997-83, Humboldt Universitaet Berlin.
  5. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
  6. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany. [Downloadable!]
  7. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  8. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March. [Downloadable!] (restricted)
  9. Paul Embrechts, 1996. "Actuarial versus Financial Pricing of Insurance," Center for Financial Institutions Working Papers 96-17, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
    Other versions:
  11. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  12. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
  13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
  15. Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 241-261, June. [Downloadable!]
Full references

Cited by:
(explanations, 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.)

  1. Vicky Henderson, 2002. "Analytical Comparisons of Option prices in Stochastic Volatility Models," OFRC Working Papers Series 2002mf03, Oxford Financial Research Centre. [Downloadable!]
  2. W. Härdle & T. Kleinow & A. Korostelev & C. Logeay, . "Semiparametric Diffusion Estimation and Application to a Stock Market Index," Sonderforschungsbereich 373 2001-24, Humboldt Universitaet Berlin.
  3. E. Platen, . "A Minimal Financial Market Model," Sonderforschungsbereich 373 2000-91, Humboldt Universitaet Berlin.
    Other versions:
  4. 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. [Downloadable!]
  5. Vicky Henderson & David Hobson, 2001. "Passport options with stochastic volatility," Applied Mathematical Finance, Taylor and Francis Journals, vol. 8(2), pages 97-118, May. [Downloadable!] (restricted)
  6. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April. [Downloadable!] (restricted)
  7. Wolfgang Hardle & Torsten Kleinow & Alexander Korostelev & Camille Logeay & Eckhard Platen, 2001. "Semiparametric Diffusion Estimation and Application to a Stock Market Model," Research Paper Series 51, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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