On a constant related to American type options
Author:
Georgiĭ Shevchenko
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 82 (2011), 171-175
MSC (2010):
Primary 60G40; Secondary 60J65, 35R35
DOI:
https://doi.org/10.1090/S0094-9000-2011-00836-8
Published electronically:
August 5, 2011
Full-text PDF Free Access
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Additional Information
Abstract: We discuss a constant which arises in several problems related to optimal exercise of American derivative securities.
References
- Mark Broadie and Jérôme Detemple, The valuation of American options on multiple assets, Math. Finance 7 (1997), no. 3, 241–286. MR 1459060, DOI https://doi.org/10.1111/1467-9965.00032
- Matthias Ehrhardt and Ronald E. Mickens, A fast, stable and accurate numerical method for the Black-Scholes equation of American options, Int. J. Theor. Appl. Finance 11 (2008), no. 5, 471–501. MR 2450224, DOI https://doi.org/10.1142/S0219024908004890
- J. D. Evans, R. Kuske, and Joseph B. Keller, American options of assets with dividends near expiry, Math. Finance 12 (2002), no. 3, 219–237. MR 1910594, DOI https://doi.org/10.1111/1467-9965.02008
- P. V. Johnson, N. J. Sharp, P. W. Duck, and D. P. Newton, A new class of option: the American delayed-exercise option, VIII Encontro Brasileiro de Finanças, Rio de Janeiro, 2008.
- Damien Lamberton and Stéphane Villeneuve, Critical price near maturity for an American option on a dividend-paying stock, Ann. Appl. Probab. 13 (2003), no. 2, 800–815. MR 1970287, DOI https://doi.org/10.1214/aoap/1050689604
- Yuliya Mishura and Georgiy Shevchenko, The optimal time to exchange one asset for another on finite interval, Optimality and risk—modern trends in mathematical finance, Springer, Berlin, 2009, pp. 197–210. MR 2648604, DOI https://doi.org/10.1007/978-3-642-02608-9_10
- S. Villeneuve, Exercise regions of American options on several assets, Finance Stoch. 3 (1999), no. 3, 295–322.
- Paul Wilmott, Sam Howison, and Jeff Dewynne, The mathematics of financial derivatives, Cambridge University Press, Cambridge, 1995. A student introduction. MR 1357666
References
- M. Broadie and J. Detemple, The valuation of American options on multiple assets, Math. Finance 7 (1997), no. 3, 241–286. MR 1459060 (98b:90012)
- M. Ehrhardt and R. E. Mickens, A fast, stable and accurate numerical method for the Black–Scholes equation of American options, Int. J. Theor. Appl. Finance 11 (2008), no. 5, 471–501. MR 2450224 (2009f:91055)
- J. Evans, R. Kuske, and J. B. Keller, American options on assets with dividends near expiry, Math. Finance 12 (2002), no. 3, 219–237. MR 1910594 (2003e:91079)
- P. V. Johnson, N. J. Sharp, P. W. Duck, and D. P. Newton, A new class of option: the American delayed-exercise option, VIII Encontro Brasileiro de Finanças, Rio de Janeiro, 2008.
- D. Lamberton and S. Villeneuve, Critical price near maturity for an American option on a dividend-paying stock, Ann. Appl. Probab. 13 (2003), no. 2, 800–815. MR 1970287 (2004d:91116)
- Y. Mishura and G. Shevchenko, The optimal time to exchange one asset for another on finite interval, Optimality and Risk — Modern Trends in Mathematical Finance. The Kabanov Festschrift (Delbaen, Freddy et al., eds.), Springer, Berlin, 2009, pp. 197–210. MR 2648604 (2011h:60096)
- S. Villeneuve, Exercise regions of American options on several assets, Finance Stoch. 3 (1999), no. 3, 295–322.
- P. Wilmott, S. Howison, and J. Dewynne, The Mathematics of Financial Derivatives. A Student Introduction, Cambridge Univ. Press, Cambridge, 1995. MR 1357666 (96h:90028)
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Additional Information
Georgiĭ Shevchenko
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email:
zhora@univ.kiev.ua
Keywords:
Optimal stopping,
geometric Brownian motion,
American option,
a free boundary problem
Received by editor(s):
February 22, 2010
Published electronically:
August 5, 2011
Additional Notes:
The author is indebted to the European Commission for support in the framework of the “Marie Curie Actions” program, grant PIRSES-GA-2008-230804
Article copyright:
© Copyright 2011
American Mathematical Society
