Analytical Approximations for the Critical Stock Prices of American Options: A Performance Comparison
AbstractMany e±cient and accurate analytical methods for pricing American options now exist. However, while they can produce accurate option prices, they often do not give accurate critical stock prices. In this paper, we propose two new analytical approximations for American options based on the quadratic approximation. We compare our methods with existing analytical methods including the quadratic approximations in Barone-Adesi and Whaley (1987) and Barone-Adesi and Elliott (1991), the lower bound approximation in Broadie and Detemple (1996), the tangent approximation in Bunch and Johnson (2000), the Laplace inversion method in Zhu (2006b), and the interpolation method in Li (2008). Both of our methods give much more accurate critical stock prices than all the existing methods above.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 15018.
Date of creation: 2009
Date of revision:
American option; Analytical approximation; Critical stock price;
Other versions of this item:
- Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, vol. 13(1), pages 75-99, April.
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
- Siim Kallast & Andi Kivinukk, 2003. "Pricing and Hedging American Options Using Approximations by Kim Integral Equations," Review of Finance, Springer, vol. 7(3), pages 361-383.
- Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-50.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
- Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 277-300.
- Khaliq, A.Q.M. & Voss, D.A. & Kazmi, S.H.K., 2006. "A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 489-502, February.
- S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
- Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages S87-S99.
- Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
- Johnson, H. E., 1983. "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 141-148, March.
- Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
- Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
- Pressacco, Flavio & Gaudenzi, Marcellino & Zanette, Antonino & Ziani, Laura, 2008. "New insights on testing the efficiency of methods of pricing and hedging American options," European Journal of Operational Research, Elsevier, vol. 185(1), pages 235-254, February.
- Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
- David S. Bunch & Herb Johnson, 2000. "The American Put Option and Its Critical Stock Price," Journal of Finance, American Finance Association, vol. 55(5), pages 2333-2356, October.
- Sullivan, Michael A, 2000. "Valuing American Put Options Using Gaussian Quadrature," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 75-94.
- Li, Minqiang, 2008. "Approximate inversion of the Black-Scholes formula using rational functions," European Journal of Operational Research, Elsevier, vol. 185(2), pages 743-759, March.
- J. D. Evans & R. Kuske & Joseph B. Keller, 2002. "American options on assets with dividends near expiry," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 219-237.
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- Minqiang Li, 2010.
"A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes,"
Review of Derivatives Research,
Springer, vol. 13(2), pages 177-217, July.
- Li, Minqiang, 2009. "A Quasi-analytical Interpolation Method for Pricing American Options under General Multi-dimensional Diffusion Processes," MPRA Paper 17348, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.