MAPPING THE TERM STRUCTURE OF INTEREST-RATES INTO A 3-DIMENSIONAL SIMPLEX

This paper presents a simple algebraic representation of the discount function as a constrained linear combination of four exponential funct ions. By restricting its three term structure coefficients within a th ree-dimensional simplex constraint set, the exponential-quadrinomial m odel guarantees the term structure to have a positive discount functio n, yield function and forward function over the entire maturity range. The model lends to a simple formula that represents the present value of any bond by a constrained linear combination of four hypothetical present values of the bond, plus a tax adjustment The formula maps the market term structure underlying the observable bonds into the simple x by a simple ordinary least squares regression.