Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-15T02:46:02.423Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis

Published online by Cambridge University Press:  06 April 2009

Michael J. Brennan  and
Eduardo S. Schwartz
Get access Rights & Permissions [Opens in a new window]

Extract

Since the seminal article by Black and Scholes on the pricing of corporate liabilities, the importance in finance of contingent claims has become widely recognized. The key to the valuation of such claims has been found to lie in the solution to certain partial differential equations. The best known of these was derived by Black and Scholes, in their original article, from the assumption that the value of the asset underlying the contingent claim follows a geometric Brownian motion.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 13 , Issue 3 , September 1978 , pp. 461 - 474
Copyright
Copyright © School of Business Administration, University of Washington 1978

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

REFERENCES

[1]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (1973), pp. 637–659.Google Scholar
[2]Boyle, P. “Options: A Monte Carlo Approach.” Journal of Financial Economics (1976).Google Scholar
[3]Brennan, M., and Schwartz, E.. “The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee.” Journal of Financial Economics, Vol. 3 (1976), pp. 195–214.CrossRefGoogle Scholar
[4]Brennan, M., and Schwartz, E.. “Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion.” Journal of Finance (1976).Google Scholar
[5]Brennan, M., and Schwartz, E.. “The Valuation of American Put Options.” Journal of Finance (1976).Google Scholar
[6]Cox, J. C., and Ross, S. A.. “The Valuation of Options for Alternative Stochastic Processes. Journal of Financial Economics, Vol. 3 (1976), pp. 145–166.CrossRefGoogle Scholar
[7]Cox, J. C., and Ross, S. A.. “A Survey of Some New Results in Financial Option Pricing Theory.” Journal of Finance, Vol. 31 (1976), pp. 383–402.Google Scholar
[8]Ingersoll, J. “A Theoretical and Empirical Investigation of the Dual Purpose Funds: An Application of Contingent Claims Analysis.” Journal of Financial Economics, Vol. 3 (1976), pp. 83–124.Google Scholar
[9]Ingersoll, J.. “A Contingent Claims Valuation of Convertible Bonds.” Unpublished Manuscript, University of Chicago (1976).Google Scholar
[10]McCracken, D., and Dorn, W.. “Numerical Methods and Fortran Programming.” New York: John Wiley and Sons, Inc. (1969).Google Scholar
[11]Merton, R. C. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, Vol. 4 (1973), pp. 141–183.Google Scholar
[12]Merton, R. C.. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance, Vol. 29 (1974), pp. 449–470.Google Scholar
[13]Parkinson, M. “Option Pricing: The American Put.” Journal of Business (1976).Google Scholar