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Free boundary and optimal stopping problems for American Asian options

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  • Andrea Pascucci

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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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File URL: http://hdl.handle.net/10.1007/s00780-007-0051-7
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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 12 (2008)
Issue (Month): 1 (January)
Pages: 21-41

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Handle: RePEc:spr:finsto:v:12:y:2008:i:1:p:21-41

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Web page: http://www.springerlink.com/content/101164/

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Related research

Keywords: American option; Asian option; Free boundary problem; Optimal stopping; 35K65; C02;

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References

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  1. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
  2. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer, vol. 31(1), pages 13-32, May.
  3. 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.
  4. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48.
  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. Jér�me Barraquand & Thierry Pudet, 1996. "Pricing Of American Path-Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51.
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Cited by:
  1. Cristina Costantini & Marco Papi & Fernanda D’Ippoliti, 2012. "Singular risk-neutral valuation equations," Finance and Stochastics, Springer, vol. 16(2), pages 249-274, April.
  2. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
  3. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer, vol. 31(1), pages 13-32, May.
  4. Daniel Sevcovic & Martin Takac, 2011. "Sensitivity analysis of the early exercise boundary for American style of Asian options," Papers 1101.3071, arXiv.org.
  5. 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.
  6. 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.
  7. 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.

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