Numerical Methods versus Bjerksund and Stensland Approximations for American Options Pricing
Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091878Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5325
 Barone-Adesi, G., R. E. Whaley, "Efficient Analytic Approximation of American Option Values,” Journal of finance, 42 (2), 1987, pp. 301-320.
 Bjerksund, P., G. Stensland, "Closed-Form Approximation of American Options,” Scandivanian Journal of Management, 9, 1993, pp. 87-99.
 Bjerksund, P., G. Stensland, "Closed-Form Valuation of American Options,” Working paper NHH, 2002.
 Black, F., M. Scholes, "The pricing of options and corporate liabilities,” Journal of Political Economy, 81, 1973, pp. 637-659.
 Boyle, P.P., "Option Valuation Using a Three Jump Process,” International Options Journal, 3, 1986, pp. 7-12.
 Brennan, M.J., E.S. Schwartz, "Finite Difference Methods and Jump Processes Arising in the Pricing of Contigent Claims: A Synthesis,” Journal of Financal and Quantitative Analysis, 25, 1978, pp. 215-227.
 Cox, J.C., S. Ross, M. Rubinstein, "Option pricing: a simplified approach,” Journal of Financial Economics, 7, 1979, pp. 229-263.
 Haug, E. G., "The complete guide to option pricing formulas,” McGraw-Hill, New-York, second edition, 2007.
 Horasali, M., "A comparison of lattice based option pricing models on the rate of convergence,” Applied Mathematics and Computation, 184(2), 2007, pp. 649-658.
 Hull, J., A. White, "Valuing Derivative Securities Using the Explicit Finite Difference Method,” Journal of Financial and Quantitative Analysis, 25(1), 1990, pp. 87-100.
 Merton, R. C., „Theory of Rational Option Pricing," The Bell Journal of Economics and Management Science, (4) 1, 1973, pp. 141-183.
 Rendleman, R. J., B. J. Bartter, "Two-State Option Pricing,” Journal of Finance, 34, 1979, pp. 1093-1110.
 Wilmott, P., "Paul Wilmott on Quantitative Finance,” John Wiley & Sons, New York, 2000.