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Path dependent volatility

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  • Pascucci, Andrea
  • Foschi, Paolo

Abstract

We propose a general class of non-constant volatility models with dependence on the past. The framework includes path-dependent volatility models such as that by Hobson&Rogers and also path dependent contracts such as options of Asian style. A key feature of the model is that market completeness is preserved. Some empirical analysis, based on the comparison with the performance of standard local volatility and Heston models, shows the effectiveness of the path dependent volatility.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 973.

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Date of creation: 30 Nov 2006
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Handle: RePEc:pra:mprapa:973

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Keywords: option pricing; stochastic volatility; path dependent option;

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References

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  1. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
  2. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547.
  3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  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.
  5. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48.
  6. 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, vol. 6(2), pages 327-43.
  7. Andrea Pascucci & Marco Di Francesco, 2005. "On the complete model with stochastic volatility by Hobson and Rogers," Finance 0503013, EconWPA.
  8. Andrea Pascucci & Paolo Foschi, 2005. "Calibration of the Hobson&Rogers model: empirical tests," Finance 0509020, EconWPA.
  9. Carl Chiarella & Oh-Kang Kwon, 2000. "A Complete Stochastic Volatility Model in the HJM Framework," Research Paper Series 43, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
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Cited by:
  1. Foschi, Paolo & Pascucci, Andrea, 2009. "Calibration of a path-dependent volatility model: Empirical tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2219-2235, April.
  2. Andrea, Pascucci, 2007. "Free boundary and optimal stopping problems for American Asian options," MPRA Paper 4766, University Library of Munich, Germany.
  3. Carey, Alexander, 2008. "Natural volatility and option pricing," MPRA Paper 6709, University Library of Munich, Germany.

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