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A More Accurate Finite Difference Approximation for the Valuation of Options

Published online by Cambridge University Press:  06 April 2009

Georges Courtadon
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Extract

Schwartz [3] proposed a model to solve for the value of a warrant or an option when a closed-form solution of the valuation equation cannot be obtained. This model is based on a difference approximation of the valuation equation and uses standard numerical methods. We intend to show here that the same methods can be used to derive a difference approximation of the solution of the valuation equation which has a greater level of accuracy than Schwartz's approximation.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 17 , Issue 5 , December 1982 , pp. 697 - 703
Copyright
Copyright © School of Business Administration, University of Washington 1982

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References

[1]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81, No. 3 (1973), pp. 637–659.CrossRefGoogle Scholar
[2]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, No. 3 (1978), pp. 461–474.Google Scholar
[3]Schwartz, E. “The Valuation of Warrants: Implementing a New Approach.” Journal of Financial Economics, Vol. 4, No. 1 (1977), pp. 79–93.Google Scholar
[4]Smith, G. D.Numerical Solutions of Partial Differential Equations. London: Oxford University Press (1978).Google Scholar