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

Language Reference

SPOT Function

calculates a column vector of spot rates given vectors of forward rates and times

SPOT( times,forward_rates)

The SPOT function returns an

vector of (per-period) spot rates.

times: is an column vector of times in consistent units. Elements should be nonnegative.
forward_rates: is an column vector of corresponding (per-period) forward rates. Elements should be positive.

The SPOT function transforms the given spot rates as

$s_i = ( \pi_{j=1}^{j=i}(1+f_j)^{t_j - t_{j-1}} )^{\frac{1}{t_i}} -1; i=2, ... ,n$

where, by convention,

For example, the following code produces the output shown:

  
    time=T(do(1,5,1)); 
    forward=T(do(0.05,0.09,0.01)); 
    spot=spot(time,forward); 
    print spot;