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A Log-Transformed Binomial Numerical Analysis Method for Valuing Complex Multi-Option Investments

Published online by Cambridge University Press:  06 April 2009

Lenos Trigeorgis
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Abstract

This paper presents a numerical method for valuing complex investments with multiple interacting options. The method is a log-transformed variation of binomial option pricing designed to overcome problems of consistency, stability, and efficiency encountered in the Cox, Ross, and Rubinstein (1979) and other numerical methods. This method handles well options with a series of exercise prices (compound options), nonproportional dividends, and interactions among a variety of real options. Comparisons with several existing numerical methods regarding accuracy, consistency, stability, and efficiency are given.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 26 , Issue 3 , September 1991 , pp. 309 - 326
Copyright
Copyright © School of Business Administration, University of Washington 1991

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References

Barone-Adesi, G., and Whaley, R.. “Efficient Analytic Approximation of American Option Values.” Journal of Finance, 42 (06 1987), 301–320.CrossRefGoogle Scholar
Black, R, and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (05–06 1973), 637–659.CrossRefGoogle Scholar
Blomeyer, E. C. “An Analytic Approximation for the American Put Price for Options on Stocks with Dividends.” Journal of Financial and Quantitative Analysis, 21 (06 1986), 229–233.CrossRefGoogle Scholar
Boyle, P. “Options: A Monte Carlo Approach.” Journal of Financial Economics, 4 (05 1977), 323–338.CrossRefGoogle Scholar
Boyle, P.“A Lattice Framework for Option Pricing with Two State Variables.” Journal of Financial and Quantitative Analysis, 23 (03 1988), 1–12.CrossRefGoogle Scholar
Brennan, M. “The Pricing of Contingent Claims in Discrete Time Models.” Journal of Finance, 34 (03 1979), 53–68.CrossRefGoogle Scholar
Brennan, M., and Schwartz, E.. “The Valuation of American Put Options.” Journal of Finance, 32 (05 1977), 449–462.CrossRefGoogle Scholar
Brennan, M., and Schwartz, E.. “Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis.” Journal of Financial and Quantitative Analysis, 13 (09 1978), 461–474.CrossRefGoogle Scholar
Cox, J.; Ross, S.; and Rubinstein, M.. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 7 (09 1979), 229–263.CrossRefGoogle Scholar
Cox, J., and Rubinstein, M.. Options Markets. Englewood Cliffs, N.J.: Prentice-Hall (1985).Google Scholar
Geske, R., and Johnson, H.. “The American Put Option Valued Analytically.” Journal of Finance, 39 (12 1984), 1511–1524.CrossRefGoogle Scholar
Geske, R., and Shastri, K.. “The Early Exercise of American Puts.” Journal of Banking and Finance (1980).Google Scholar
Geske, R., and Shastri, K.. “Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques.” Journal of Financial and Quantitative Analysis, 20 (03 1985), 45–71.CrossRefGoogle Scholar
Hull, J., and White, A.. “The Use of the Control Variate Technique in Option Pricing.” Journal of Financial and Quantitative Analysis, 23 (09 1988), 237–251.CrossRefGoogle Scholar
Jarrow, R., and Rudd, A.. Option Pricing. Homewood, IL: R. D. Irwin (1983).Google Scholar
Johnson, H. E. “An Analytic Approximation for the American Put Price.” Journal of Financial and Quantitative Analysis, 18 (03 1983), 141–148.CrossRefGoogle Scholar
Majd, S., and Pindyck, R.. “Time to Build, Option Value, and Investment Decisions.” Journal of Financial Economics, 18 (03 1987), 7–27.CrossRefGoogle Scholar
Mason, S. P. “The Numerical Analysis of Certain Free Boundary Problems Arising in Financial Economics.” Harvard Business School Working Paper 78–52 (1978).Google Scholar
Mason, S. P., and Merton, R. C.. “The Role of Contingent Claims Analysis in Corporate Finance.” In Recent Advances in Corporate Finance, Altman, E. and Subrahmanyam, M., eds. Homewood, IL: R.D. Irwin (1985).Google Scholar
McDonald, R., and Siegel, D.. “Investment and the Valuation of Firms when There is an Option to Shut Down.” International Economic Review, 26 (06 1985), 331–349.CrossRefGoogle Scholar
McDonald, R., and Siegel, D.. “The Value of Waiting to Invest.” Quarterly Journal of Economics, 101 (11 1986), 707–727.CrossRefGoogle Scholar
Myers, S. C. “Finance Theory and Financial Strategy.” Midland Corporate Finance Journal, 5 (Spring 1987), 6–13.Google Scholar
Myers, S. C, and Majd, S.. “Abandonment Value and Project Life.” Advances in Futures and Options Research, 4 (1990), 1–21.Google Scholar
Omberg, E. “A Note on the Convergence of Binomial-Pricing and Compound-Option Models.” Journal of Finance, 42 (06 1987), 463–469.Google Scholar
Omberg, E. “Efficient Discrete Time Jump Process Models in Option Pricing.” Journal of Financial and Quantitative Analysis, 23 (06 1988), 161–174.CrossRefGoogle Scholar
Parkinson, M. “Option Pricing: The American Put.” Journal of Business, 50 (01 1977), 21–36.CrossRefGoogle Scholar
Rendleman, R., and Bartter, B.. “Two-State Option Pricing.” Journal of Finance, 34 (12 1979), 1093–1110.Google Scholar
Trigeorgis, L. “Valuing Real Investment Opportunities: An Options Approach to Strategic Capital Budgeting.” Unpubl. Ph.D. Diss., Harvard Univ. (1986).Google Scholar
Trigeorgis, L. “A Conceptual Options Framework for Capital Budgeting.” Advances in Futures and Options Research, 3 (1988), 145–167.Google Scholar
Trigeorgis, L. “Option Interactions and the Valuation of Investments with Multiple Real Options.” Paper presented at the 1990 American Finance Association conference, Washington, D.C.CrossRefGoogle Scholar
Trigeorgis, L., and Mason, S. P.. “Valuing Managerial Flexibility.” Midland Corporate Finance Journal, 5 (Spring 1987), 14–21.Google Scholar