101 Concepts for the Level I Exam

Essential Concept 78: Interest Rate Swaps

A swap is an over-the-counter contract between two parties to exchange a series of cash flows based on some pre-determined formula. In a plain vanilla interest rate swap one party pays fixed rate, whereas the other party pays a floating rate.

Swap fixed rate = (1 – final discount factor) / (sum of all discount factors)

Value of a fixed rate swap at Time t = Sum of the present value of the difference in fixed swap rates x Stated notional amount

$\mathrm{V=NA}\left({\mathrm{FS}}_0\mathrm{-}{\mathrm{FS}}_{\mathrm{t}}\right)\left({\mathrm{d}}_{\mathrm{1}}\mathrm{+}{\mathrm{d}}_{\mathrm{2}}\mathrm{+}{\mathrm{d}}_{\mathrm{3}}\mathrm{+\dots +}{\mathrm{d}}_{\mathrm{n}}\right)$

Example: Suppose two years ago we entered a €100,000,000 seven-year receive-fixed Libor-based interest rate swap with annual resets using 30/360 day count. The fixed rate in the swap contract at initiation was 3%. Using the present value factors in the below given table, what is the value for the party receiving the fixed rate?

Maturity (years)	Present Value Factors
1	0.9906
2	0.9789
3	0.9674
4	0.9556
5	0.9236

Solution: We first compute the new swap fixed rate. The sum of the present values is 4.8161. Therefore, the fixed swap rate is:

$\mathrm{r}}_{\mathrm{FIX}}\mathrm{=}\frac{\mathrm{1-0.9236}}{\mathrm{4.8161}}\mathrm{=1.59\%}.$

$\[\mathrm{V=NA}\left({\mathrm{FS}}_0\mathrm{-}{\mathrm{FS}}_{\mathrm{t}}\right)\left({\mathrm{d}}_{\mathrm{1}}\mathrm{+}{\mathrm{d}}_{\mathrm{2}}\mathrm{+}{\mathrm{d}}_{\mathrm{3}}\mathrm{+\dots +}{\mathrm{d}}_{\mathrm{n}}\right)$