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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.

Suggested Citation

  • Andrea, Pascucci, 2007. "Free boundary and optimal stopping problems for American Asian options," MPRA Paper 4766, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:4766
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    3. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(1), pages 13-32, 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, January.
    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, January.
    6. Lixin Wu & Yue Kuen Kwok & Hong Yu, 1999. "Asian Options With The American Early Exercise Feature," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 101-111.
    7. Rongwen Wu & Michael C. Fu, 2003. "Optimal Exercise Policies and Simulation-Based Valuation for American-Asian Options," Operations Research, INFORMS, vol. 51(1), pages 52-66, February.
    8. 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.
    9. Jérôme Barraquand & Thierry Pudet, 1996. "Pricing Of American Path‐Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51, January.
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    Citations

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    Cited by:

    1. Zaevski, Tsvetelin S., 2019. "A new form of the early exercise premium for American type derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 338-340.
    2. Daniel Sevcovic & Martin Takac, 2011. "Sensitivity analysis of the early exercise boundary for American style of Asian options," Papers 1101.3071, arXiv.org.
    3. Cristina Costantini & Marco Papi & Fernanda D’Ippoliti, 2012. "Singular risk-neutral valuation equations," Finance and Stochastics, Springer, vol. 16(2), pages 249-274, April.
    4. Frank Wusterhausen, 2015. "An Analysis of Path-Dependent Options," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 874-887, December.
    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. Mabel C. Chou & Mahmut Parlar & Yun Zhou, 2017. "Optimal Timing to Initiate Medical Treatment for a Disease Evolving as a Semi-Markov Process," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 194-217, October.
    7. 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.
    8. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    9. Paolo Foschi & Andrea Pascucci, 2008. "Path dependent volatility," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 31(1), pages 13-32, May.
    10. Francesco Rotondi, 2019. "American Options on High Dividend Securities: A Numerical Investigation," Risks, MDPI, vol. 7(2), pages 1-20, May.
    11. 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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    More about this item

    Keywords

    optimal stopping; free boundary; Asian option; American option;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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