FM for Actuaries

Spot Rates, Forward Rates and the Term Structure 95
Table 3.2: Computation results for Example 3.12
t i S t i F t i F t (1 + iS t )−t (1 + i S t )−t
1 0.035000 0.035000 0.033816 0.966184
2 0.038000 0.041009 0.038061 0.928122
3 0.043000 0.053072 0.046775 0.881347
4 0.049000 0.067208 0.055503 0.825844
5 0.052000 0.064086 0.049738 0.776106
Total 0.223894 4.377604
Example 3.13: Consider the swap contract in Example 3.12. Instead of a level
notional amount of $1 million, the notional amounts m t for t =1, 2, 3, 4 and 5
are now assumed to be $1 million, $2 million, ···, and $5 million, respectively.
Determine the swap rate of this accreting swap.
Solution: Table 3.3 shows the computation of the swap rate via equation (3.32).
Hence,
R S = 0.720965
12.650379 =5.6992%.
Table 3.3: Computation results for Example 3.13
t i S t i F t m t m t i F t (1 + iS t )−t m t (1 + i S t )−t
1 0.035000 0.035000 1 0.033816 0.966184
2 0.038000 0.041009 2 0.076122 1.856245
3 0.043000 0.053072 3 0.140326 2.644042
4 0.049000 0.067208 4 0.222013 3.303376
5 0.052000 0.064086 5 0.248688 3.880532
Total 0.720965 12.650379
A deferred swap is an interest rate swap for which the exchange of interest
payments starts after a deferred period. The swap rate and the length of the deferred
period are determined at time 0, the moment when the two parties enter into the
contract. The cash flows of the market maker of a deferred swap with a deferred