Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-03T01:39:05.614Z Has data issue: false hasContentIssue false
  • English
  • Français

A Lattice Framework for Option Pricing with Two State Variables

Published online by Cambridge University Press:  06 April 2009

Phelim P. Boyle
Get access Rights & Permissions [Opens in a new window]

Abstract

A procedure is developed for the valuation of options when there are two underlying state variables. The approach involves an extension of the lattice binomial approach developed by Cox, Ross, and Rubinstein to value options on a single asset. Details are given on how the jump probabilities and jump amplitudes may be obtained when there are two state variables. This procedure can be used to price any contingent claim whose payoff is a piece-wise linear function of two underlying state variables, provided these two variables have a bivariate lognormal distribution. The accuracy of the method is illustrated by valuing options on the maximum and minimum of two assets and comparing the results for cases in which an exact solution has been obtained for European options. One advantage of the lattice approach is that it handles the early exercise feature of American options. In addition, it should be possible to use this approach to value a number of financial instruments that have been created in recent years.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 23 , Issue 1 , March 1988 , pp. 1 - 12
Copyright
Copyright © School of Business Administration, University of Washington 1988

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.)

References

Boyle, P. P., and Kirzner, E. F.. “Pricing Complex Options: Echo-Bay Ltd. Gold Purchase Warrants.” Canadian Journal of Administrative Sciences, 2 (12 1985), 294–306.CrossRefGoogle Scholar
Brennan, M. J., and Schwartz, E. S.. “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
Budd, N. “The Future of Commodity Indexed Financing.” Harvard Business Review, 61 (07–08 1983), 44–50.Google Scholar
Cox, J.; Ross, S.; and Rubinstein, M.. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 7 (10 1979), 229–264.CrossRefGoogle Scholar
Geske, R., and Johnson, H. E.. “The American Put Option Valued Analytically.” The Journal of Finance, 39 (12 1984), 1511–1524.CrossRefGoogle 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 Pricing of Options on Assets with Stochastic Volatilities.” Journal of Finance, 42 (06 1987), 281–300.CrossRefGoogle Scholar
Johnson, H. “Pricing Complex Options.” Mimeo, Dept. of Finance, College of Business Administration, Louisiana State Univ., Baton Rouge, LA (1981).Google Scholar
Johnson, H. “Options on the Maximum or the Minimum of Several Assets.” Journal of Financial and Quantitative Analysis, 22 (09 1987), 277–283.CrossRefGoogle Scholar
Johnson, H., and Shanno, D.. “Option Pricing when the Variance is Changing.” Journal of Financial and Quantitative Analysis, 22 (06 1987), 143–151.CrossRefGoogle Scholar
Parkinson, M. “Option Pricing: The American Put.” Journal of Business, 50 (06 1977), 21–36.CrossRefGoogle Scholar
Schwartz, E. S. “The Pricing of Commodity Linked Bonds.” Journal of Finance, 37 (05 1982), 525–541.Google Scholar
Stapleton, R. C, and Subrahmanyan, M. G.. “The Valuation of Options when Asset Returns are Generated by a Binomial Process.” The Journal of Finance, 39 (12 1984), 1525–1540.CrossRefGoogle Scholar
Stulz, R. M. “Options on the Minimum or the Maximum of Two Risky Assets: Analysis and Applications.” Journal of Financial Economics, 10 (07 1982), 161–185.CrossRefGoogle Scholar
Stulz, R. M., and Johnson, H.. “An Analysis of Secured Debt.” Journal of Financial Economics, 14 (12 1985), 501–521.CrossRefGoogle Scholar
Wiggins, J. “Stochastic Variance Option Pricing.” Working Paper, Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA (1985).Google Scholar