ABSTRACT
The practice of modern finance theory depends on an ability to generate accurate and timely forecasts of asset returns. In this field, considerable effort has been expended to base the generation of asset returns on a set of state variables driven by the dynamics of the environment.
This requires the solution of a fundamental parabolic partial differential equation, often with variable coefficient, and with a wide range of specification of boundary and initial value conditions. A major drawback in financial management of large, real-time problems of this sort is that they require numerical intensive computing. Approximations or simplifications are used. The one state variable model of Black and Scholes [Bla73] leads to a closed form solution of the value of a call option, as explored in an APL solution by Bogart [Bog87].
The two state variable model of Brennan and Schwartz [Bre79, Sch84] determines the value of an intermediate maturity bond whose value depends upon the dynamic evolution of: a short-term rate, such as the 3 month Treasury Bill rate, and a long term rate, such as the 30 year Treasury bond rate. This solution does not have a closed form and must be solved numerically or approximately.
This paper describes a formulation of the Brennan and Schwartz model; develops a finite difference representation; describes the strategy for an APL2 implementation; and illustrates the results with the run of an application.
- Ayb79.Ayres, H. R. and J. Y. Barry, "The Equilibrium Yield Curve for Government Securities," Financial Analysts Journal May/June 1979, 31-39.Google Scholar
- Bla73.Black, F. and M. Scholes, "The Pricing of Options and Corporate Liabilities," Journal of Political Economy 81 (1973), 637-659.Google ScholarCross Ref
- Bog87.Bogart, B., "OPERA, Options Price Evaluation and Risk Analysis System," APL87 Conference Proceedings, 478-486. Google ScholarDigital Library
- Bre79.Brennan, M. J. and E. S. Schwartz, "A Continuous Time Approach to the Pricing of Bonds," Journal of Banking and Finance 3 (1979), 133-155.Google Scholar
- Bre78."Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis (September 1978), 461-474.Google Scholar
- Cox78.Cox, J. C., J. E. Ingersoll, and S. A. Ross, "A Theory of the Term Structure of Interest Rates," Research Paper No. 468, Graduate School of Business, Stanford University, 1978.Google Scholar
- Mck70.McKee, S. and A. R. Mitchell, "Alternative Direction Methods for Parabolic Equations in Two Space Dimensions with Mixed Derivatives,*' Computer Journal 13.1 (February 1970), 81-86.Google Scholar
- Sch84.Schaeffer, S. M. and E.S. Schwartz, "A Two-Factor Model of the Term Structure: An Approximiate Analytical Solution," Mime0 , London Business School, 1984.Google ScholarCross Ref
Index Terms
- APL2 implementation of numerical asset pricing models
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APL2 implementation of numerical asset pricing models
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