Hostname: page-component-7f64f4797f-7vqc4 Total loading time: 0 Render date: 2025-11-03T15:45:16.698Z Has data issue: false hasContentIssue false
  • English
  • Français

Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques

Published online by Cambridge University Press:  06 April 2009

Robert Geske  and
Kuldeep Shastri
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to compare a variety of approximation techniques for valuing contingent contracts when analytic solutions do not exist. The comparison is made with respect to the differences in both the approximation theory and the efficiency of the computation algorithms. The focus of the computational comparison is upon binomial and finite difference methods applied to option valuation models with one stochastic variable. However, many of the results would generalize to pricing corporate securities, and also to certain aspects of problems involving multiple stochastic variables.

Information

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 20 , Issue 1 , March 1985 , pp. 45 - 71
Copyright
Copyright © School of Business Administration, University of Washington 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Abramowitz, M., and Stegum, I.. Handbook of Mathematical Functions. National Bureau of Standards (1970).Google Scholar
[2]Ames, William F.Numerical Methods for Partial Differential Equations. Academic Press, (1977).Google Scholar
[3]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (05–06 1973), pp. 637–659.Google Scholar
[4]Boyle, P. “Options: A Monte Carlo Approach.” Journal of Financial Economics, Vol. 44 (05 1977), pp. 323–338.Google Scholar
[5]Brennan, M., and Schwartz, E.. “The Valuation of American Put Options.” Journal of Finance, Vol. 32 (05 1977), pp. 449–462.Google Scholar
[6]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, Vol. 13 (09 1978), pp. 461–474.Google Scholar
[7]Brennan, M., and Schwartz, E.. “Convertible Bonds: Valuattion and Optimal Strategies for Call and Conversion.” Journal of Finance, Vol. 32 (12 1977), pp. 1699–1716.Google Scholar
[8]Courtedon, G. “A More Accurate Finite Difference Approximation for the Valuation of Options.” Journal of Financial and Quantitative Analysis, Vol. 17 (12 1982), pp. 697–705.Google Scholar
[9]Cox, J. “Note on Option Pricing 1: Constant Elasticity of Variance Diffusions.” Stanford, Unpublished (1975).Google Scholar
[10]Cox, J., and Ross, S.. “The Valuation of Option for Alternative Stochastic Processes.” Journal of Financial Economics, Vol. 3 (03 1976), pp. 145–166.Google Scholar
[11]Cox, J., Ross, S., and Rubinstein, M.. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, Vol. 7 (10 1979), pp. 229–264.Google Scholar
[12]Cox, J., and Rubinstein, M.. Option Markets. Englewood Cliffs, NJ: Prentice Hall (1984).Google Scholar
[13]Dahlquist, G., and Bjorck, A.. Numerical Methods. Prentice Hall (1974).Google Scholar
[14]Feller, W.An Introduction to Probability Theory and Its Applications. Vol. 1. New York: John Wiley and Sons (1968).Google Scholar
[15]Friedman, A.Partial Differential Equations. Huntington, NY: Robert Krieger Publications (1976).Google Scholar
[16]Garman, M. “A General Theory of Asset Valuation Under Diffusion State Processes.” Working Paper No. 50, University of California, Berkeley (1976).Google Scholar
[17]Geske, R. “The Valuation of Compound Options.” Journal of Financial Economics, Vol. 7 (03 1979), pp. 63–81.Google Scholar
[18]Geske, R. “A Note on an Analytical Method for the Valuation of American Call Options on Dividend Paying Stocks.” Journal of Financial Economics, Vol. 7 (12 1979), pp. 275–380.Google Scholar
[19]Geske, R., and Shastri, K.. “The Effects of Payouts on the Rational Pricing of American Options.” Working Paper, University of California, Los Angeles (1982).Google Scholar
[20]Geske, R., and Shastri, K.. “The Early Exercise of American Puts.” The Journal of Banking and Finance, Vol. 9 (01 1985).CrossRefGoogle Scholar
[21]Geske, R., and Johnson, H.. “The American Put Valued Analytically.” Journal of Finance, Vol. 39 (12 1984), pp. 1511–1524.Google Scholar
[22]Ingersoll, J. “A Contingent-Claims Valuation of Convertible Securities.” Journal of Financial Economics, Vol. 4 (05 1977), pp. 289–322.Google Scholar
[23]Johnson, H. “An Analytic Approximation to the American Put Price.” The Journal of Financial and Quantitative Analysis, Vol. 17 (03 1983), pp. 141–148.Google Scholar
[24]Mason, S. “The Numerical Analysis of Certain Free Boundary Problems Arising in Financial Economics.” Working Paper 78–52, Harvard Business School (1978).Google Scholar
[25]Merton, R. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, Vol. 4 (Spring 1973), pp. 141–183.Google Scholar
[26]Merton, R. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance, Vol. 29 (05 1974), pp. 449–470.Google Scholar
[27]Merton, R. “Options Pricing when the Underlying Stock Returns are Discontinuous.” Journal of Financial Economics, Vol. 31 (03 1976), pp. 333–350.Google Scholar
[28]Parkinson, M. “Option Pricing: The American Put,” Journal of Business, Vol. 50 (01 1977), pp. 21–36.Google Scholar
[29]Roll, R. “An Analytic Method for Valuing American Call Options on Dividend Paying Stocks.” Journal of Financial Economics, Vol. 85 (11 1977), pp. 251–258.Google Scholar
[30]Rubinstein, M. “Displaced Diffusion Option Pricing.” Journal of Finance, Vol. 38 (03 1983), pp. 213–218.Google Scholar
[31]Schwartz, E. “The Valuation of Warrants: Implementing a New Approach.” Journal of Financial Economics, Vol. 4 (01 1977), pp. 79–94.CrossRefGoogle Scholar
[32]Sommerfield, A.Partial Differential Equations in Physics. New York: Academic Press (1949).Google Scholar
[33]Whaley, R. “On the Valuation of American Call Options on Stocks with Known Dividends.” Journal of Financial Economics, Vol. 10 (06 1981), pp. 207–211.CrossRefGoogle Scholar