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On the complete model with stochastic volatility by Hobson and Rogers

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Author Info
Andrea Pascucci
Marco Di Francesco

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Abstract

We examine a recent model, proposed by Hobson and Rogers, which generalizes the classical one by Black and Scholes for pricing derivative securities such as options and futures. We treat the numerical solution of some degenerate partial differential equations governing this financial problem and propose some new numerical schemes which naturally apply in this degenerate setting. Then we aim to emphasize the mathematical tractability of the Hobson-Rogers model by presenting analytical and numerical results comparable with the known ones in the classical Black-Scholes environment.

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File URL: http://129.3.20.41/eps/fin/papers/0503/0503013.pdf
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Paper provided by EconWPA in its series Finance with number 0503013.

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Length: 12 pages
Date of creation: 11 Mar 2005
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Handle: RePEc:wpa:wuwpfi:0503013

Note: Type of Document - pdf; pages: 12
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Web page: http://129.3.20.41

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Related research
Keywords: Black-Scholes model; stochastic volatility; path-dependent option; hypoelliptic equation;

Find related papers by JEL classification:
G - Financial Economics

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. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  3. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  4. 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 637-54, May-June. [Downloadable!] (restricted)
  5. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley. [Downloadable!]
  6. Fabio Antonelli & Andrea Pascucci, 2005. "On the viscosity solutions of a stochastic differential utility problem," Finance 0503021, EconWPA. [Downloadable!]
  7. Emilio Barucci & Paul Malliavin & Maria Elvira Mancino & Roberto Renò & Anton Thalmaier, 2003. "The Price-Volatility Feedback Rate: An Implementable Mathematical Indicator of Market Stability," Mathematical Finance, Blackwell Publishing, vol. 13(1), pages 17-35. [Downloadable!] (restricted)
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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. Andrea Pascucci & Paolo Foschi, 2005. "Calibration of the Hobson&Rogers model: empirical tests," Finance 0509020, EconWPA. [Downloadable!]
  2. Pascucci, Andrea & Foschi, Paolo, 2006. "Path dependent volatility," MPRA Paper 973, University Library of Munich, Germany. [Downloadable!]
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