APL2 implementation of numerical asset pricing models

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.