Forward Interest Rates: Discount Factors and Term Yields

Summary

The note compares two ways to calculate a forward interest rate between maturities. One derives the rate from the ratio of discount factors over the interval; the other uses the change in maturity-weighted term yields divided by the time difference. It explains that the yield-based expression is a linear approximation when discount factors are represented by continuously compounded term yields.

The discount-factor formula is identified as the generally correct calculation, while the yield expression is an approximation. The distinction matters because term yields and discount factors encode compounding differently. The discussion is brief and does not specify day-count conventions, compounding assumptions, or market details, so those must be aligned when applying the formulas to actual instruments.

Key ideas

• The discount-factor ratio gives the forward rate over the interval between two maturities.
• The term-yield expression is a linear approximation under the stated exponential discount-factor assumption.
• Use consistent maturity units and conventions when calculating practical forward rates.

Tags

# Interest Rate forward calculation


# Interest Rate forward calculation












I have come across two formulas for the forward interest rate computation.These are given below. 1)((Df1/Df2)-1)/(T2-T1) 2) (R2T2-R1T1)/(T2-T1)

I do not understand when should i use which one of the above formulas. Any help would be appreciated!! Thank you

## Answer by achirikhin (score 1, accepted)

https://quant.stackexchange.com/a/79265

Option 2 is the linear approximation of Option 1, if R is the term yield; assume Df(t) = exp(-R(t)t)

Option 1 is always correct

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.