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Free boundary and optimal stopping problems for American Asian options

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  • Andrea, Pascucci

Abstract

We give a complete and self-contained proof of the existence of a strong solution to the free boundary and optimal stopping problems for pricing American path dependent options. The framework is su±ciently general to include geometric Asian options with non-constant volatility and recent path-dependent volatility models.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 4766.

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Date of creation: 07 Sep 2007
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Handle: RePEc:pra:mprapa:4766

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Keywords: optimal stopping; free boundary; Asian option; American option;

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References

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  1. Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
  2. Jér�me Barraquand & Thierry Pudet, 1996. "Pricing Of American Path-Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51.
  3. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
  4. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer, vol. 31(1), pages 13-32, May.
  5. Min Dai & Yue Kuen Kwok, 2006. "Characterization Of Optimal Stopping Regions Of American Asian And Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 63-82.
  6. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48.
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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. Pascucci, Andrea & Foschi, Paolo, 2006. "Path dependent volatility," MPRA Paper 973, University Library of Munich, Germany.
  3. Calvo-Garrido, Maria del Carmen & Pascucci, Andrea & Vázquez Cendón, Carlos, 2012. "Mathematical analysis and numerical methods for pricing pension plans allowing early retirement," MPRA Paper 36494, University Library of Munich, Germany.
  4. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
  5. Daniel Sevcovic & Martin Takac, 2011. "Sensitivity analysis of the early exercise boundary for American style of Asian options," Papers 1101.3071, arXiv.org.
  6. Tomas Bokes & Daniel Sevcovic, 2009. "Early exercise boundary for American type of floating strike Asian option and its numerical approximation," Papers 0912.1321, arXiv.org.
  7. Cristina Costantini & Marco Papi & Fernanda D’Ippoliti, 2012. "Singular risk-neutral valuation equations," Finance and Stochastics, Springer, vol. 16(2), pages 249-274, April.

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