When an interest rate swap is contracted, its initial value is zero. However, after some time passes, its value may become positive or negative for one of the parties.
A swap involves the exchange of fixed and floating interest income between the two parties, and it does not involve the exchange of the loan principal (since they are equal). However, if we assume that the principals are also exchanged, then the value of the swap can be interpreted as the sum of the values of the exchanged loans.
When valuing a floating-rate loan, it helps to note that the value of such a bond right after an interest payment is equal to its nominal (par) value, because the discount factor and the yield are identical at that moment.
📈 In the diagram, the value of the bond at the time of the first payment is shown, and it can be discounted using the Zero-Coupon Swap Rate for the corresponding period. Note also that the rate ( k^* ) is known in advance, since according to the contract, the exchange is based on the floating rate prevailing at the beginning of the period.
Example:
Another method for valuing an Interest Rate Swap is to arrange the cash flows according to Forward Rate Agreement (FRA) contracts and then value these cash flows using the FRA valuation methodology.
An FRA is valued under the assumption that the agreed-upon forward rates will be realized in the future. The valuation table therefore takes the following form:
In the fixed cash flow section, only interest payments are listed, while for the floating cash flows, the corresponding forward rates are derived. Transitional formulas can be found in the Excel file:
Source: Options, Futures & Other Derivatives — John C. Hull
Leave a Reply