Language Reference: RATES Function :: SAS/IML(R) 9.2 User's Guide

Language Reference

RATES Function

calculates a column vector of (per-period, such as per-year) interest rates converted from one base to another

RATES( rates,oldfreq,newfreq)

The RATES function returns an

vector of interest rates converted from one base to another.

rates: is an column vector of rates corresponding to the old base. Elements should be positive.
oldfreq: is a scalar that represents the old base. If positive, it represents discrete compounding as the reciprocal of the number of compoundings per period. If zero, it represents continuous compounding. If -1, the rates represent discount factors. No other negative values are accepted.
newfreq: is a scalar that represents the new base. If positive, it represents discrete compounding as the reciprocal of the number of compoundings per period. If zero, it represents continuous compounding. If -1, the rates represent discount factors. No other negative values are accepted.

Let

be the discount function, which is the present value of a unit amount to be received

periods from now. The discount function can be expressed in three different ways:

with per-period discount factors

with continuous compounding:

$d(t) = e^{-r_t t}$

with discrete compounding:

$d(t) = (1+fr)^{-t/f}$

where $0 \lt f \lt 1$ is the frequency, the reciprocal of the number of compoundings per period. The RATES function converts between these three representations.

For example, the following code uses the RATES function:

  
    rates=T(do(0.1,0.3,0.1)); 
    oldfreq=0; 
    newfreq=0; 
    rates=rates(rates,oldfreq,newfreq); 
    print rates;

The output is as follows:

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