Abstract
Finite difference schemes have proved to be very flexible numerical methods for the pricing of contingent claims with one and two underlying state variables. This flexibility and the steady stream of new complex financial instruments imply that finite difference schemes for the valuation of contingent claims with three underlying state variables can supposedly be very useful. In this paper, two such schemes are developed and tested. For practical purposes, numerical valuation of contingent claims with three underlying state variables by means of finite difference methods is probably too laborious computationally to be performed on a single processor computer. Many calculations can, however, be performed in parallel. Therefore, the methods are well suited to be executed on a massively parallel computer, like the Connection Machine CM-200, which is used in this paper. The accuracy of the schemes proposed in this paper suggests that valuation of multivariate contingent claims with the help of finite difference methods on a massively parallel computer can be a useful approach for academics as well as practitioners.
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References
Bailey, J., 1990, Implementing Fine-grained Scientific Algorithms on the Connection Machine Super Computer, Thinking Machines Technical Report Series TR90-1, Thinking Machines Corporation, Cambridge, Massachusetts.
Boghosian, B.M., 1990, Computational Physics on the Connection Machine, Massive parallelism — a new paradigm,Computers in Physics, Jan./Feb.
Boyle, P.P., 1988, A Lattice Framework for Option Pricing with Two State Variables,J. Financial and Quantitative Anal. 23, 1–12.
Boyle, P.P., Evnine, E. and Gibbs, S., 1989, Numerical Evaluation of Multivariate Contingent Claims,The Review of Financial Studies,2(2), 241–250.
Ekvall, N., 1993,Studies in Complex Financial Instruments and their Valuation, Ph.D. dissertation, Stockholm School of Economics.
Foster, G.H., 1989, Bond Pricing in APL2: A Study in Numerical Solution of the Brennan and Schwartz Bond Pricing Model using a Vector Processor,Computer Science in Economics and Management 2(3), 179–196.
Geske, R. and Shastri, K., 1985, Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques,J. Financial and Quantitative Anal. 20, 45–71.
Hockney, R.W. and Jesshope, C.R., 1988,Parallel Computers 2, 2nd edition, Adam Hilger, Bristol.
Hull, J. (1989),Options, Futures, and other Derivative Securities, Prentice-Hall, Englewood Cliffs, NJ.
Hull, J. and White, A., 1990, Valuing Derivative Securities Using the Explicit Finite Difference Method,J. Financial and Quantitative Anal. 25, 87–100.
Jennergren, L.P. and Näslund, B., 1990, Models for the Valuation of International Convertible Bonds,J. International Financial Management and Accounting 2:2 & 3, 93–110.
Jennergren, L.P. and Sörensson, T., 1991, Choice of Model in Convertible Valuation—A Case Study,Omega 4, 185–191.
Johnson, H., 1987, Options on the Maximum or the Minimum of Several Assets,J. Financial and Quantitative Anal. 22, 277–283.
Marchuk, G.I., 1990, Splitting and Alternating Direction Methods, in P.G. Ciarlet and J.L. Lions (eds),Handbook of Numerical Analysis, vol. I, North Holland, Amsterdam, 197–462.
McConnel, J.J. and Schwartz, E.S., 1986, LYON Taming,J. Finance 61, 561–576.
Merton, R.C., 1974, On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,J. Finance 29, 449–470.
Merton, R.C., 1977, On the Pricing of Contingent Claims and The Modigliani-Miller Theorem,J. Financial Economics 5, 241–250.
Schwartz, E.S., 1977, The Valuation of Warrants: Implementing a New Approach,J. Financial Economics 4, 79–93.
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Ekvall, N. Experiences in the pricing of trivariate contingent claims with finite difference methods on a massively parallel computer. Comput Econ 7, 63–72 (1994). https://doi.org/10.1007/BF01299567
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DOI: https://doi.org/10.1007/BF01299567