Discount Factors
Another important concept is that of a discount factor between two times The discount factors are, of course, fundamental quantities used in present value calculations, it is useful to apply a double indexing system to the discount factors paralleling the system used for forward rates Accordingly, the symbol dj k denotes the discount factor used to discount cash received at time k back to an equivalent amount of cash at time j The normal, time zero, discount factors are d\ = do i, d2 ~ do 2, . ., d„ = do „ The discount factors can be expressed in terms of the forward rates as
The discount factors are related by a compounding rule: to discount from time k back to time /, one can first discount from time k back to an intermediate time j and then discount from j back to /. In other words, dik — d, jdj k for i < j < k.
Discount factor relation The discount factor between periods i and j is defined as djj =
These factors satisfy the compounding rule d, k = dijdj k for i < j < k.
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