consistent with what we said in the previous chapter, when interest rates increase (as they did in our illustration), the fixed-rate payer benefits because the value of the swap increases. In contrast, the fixed-rate receiver must make payments with a present value of $11,459,495 but will only receive fixed-rate payments with a present value equal to $9,473,390. Thus, the value of the swap for the fixed-rate receiver is -$1,986,105. Again, as explained earlier, the fixed-rate receiver is adversely affected by a rise in interest rates because it results in a decline in the value of a swap.             The same valuation principle applies to more complicated swaps. For example, there are swaps whose notional amount changes in a pre- determined way over the life of the swap. These include amortizing swaps, accreting swaps, and roller coaster swaps. Once the payments are specified, the present value is calculated as described above by sim- ply adjusting the payment amounts by the changing notional amounts- the methodology does not change.       PRIMARY DETERMINANTS OF SWAP SPREADS   As we have seen, interest rate swaps are valued using no-arbitrage rela- tionships relative to instruments (funding or investment vehicles) that produce the same cash flows under the same circumstances. Earlier we provided two interpretations of a swap: (1) a package of futures/forward contracts and (2) a package of cash market instruments. The swap spread is defined as the difference between the swaps fixed rate and the rate on a Treasury whose maturity matches the swaps tenor. Exhibit 12.10 displays a Bloomberg screen with interest rate swap rates (in percent) and swap spreads (in basis points) for various maturities out to price is the fixed rate that the bro-     7, 2001. This plot can be obtained using the function USSP5 Index GP. The swap spread is determined by the same factors that drive the