An FRA is a contract between two parties that determines the interest rate to be paid on a future date, based on a reference rate such as LIBOR. An IRS is a contract between two parties that involves exchanging fixed and floating interest payments over a period of time, based on a reference rate such as LIBOR.
The pricing link between FRAs and IRSs is that both contracts are based on the same reference rate, and both contracts have a zero net present value at inception. This means that the fixed rate in an IRS, also known as the swap rate, is equal to the weighted average of the FRA rates for the same period. In other words, the swap rate is the rate that makes the present value of the fixed payments equal to the present value of the floating payments.
Basic Theory:
- Forward Rate Agreements (FRAs): FRAs are financial contracts where two parties agree to exchange interest rate payments at a future date. The agreement fixes the interest rate on a notional amount for a specified period.
- Interest Rate Swaps (IRS): An Interest Rate Swap involves the exchange of fixed-rate and floating-rate interest payments between two parties. It allows entities to manage their exposure to interest rate fluctuations.
Procedure:
The pricing of FRAs and Interest Rate Swaps is interconnected. The general procedure involves:
- Determine the Forward Rate in the FRA: Use the formula for the forward rate to calculate it based on the current spot rates.
![\[ FRA = \frac{(1 + R_t \cdot \frac{T}{360})}{(1 + R_t \cdot \frac{T_{\text{start}}}{360})} - 1 \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-2e9c3f397b417036959beff5311a0997_l3.svg "Rendered by QuickLaTeX.com")
- Apply the Forward Rate to Calculate the Fixed Rate in IRS: The fixed rate in an IRS can be influenced by the forward rate from the corresponding FRA.
Fixed Rate in IRS = FRA + Spread
Explanation:
Let’s consider a scenario with the following parameters:
- Spot rate for the FRA period: 4.5%
- FRA period: 90 days
- Spread in IRS: 0.25%
Calculation in Excel:
Here’s an Excel table demonstrating the calculation:
| Description | Formula | Calculation |
|---|---|---|
| Spot Rate (R_t) | 4.5% | 0.045 |
| FRA Period (T) | 90 days | 90 |
Result: The fixed rate in the IRS, considering the FRA forward rate and spread, is approximately 5.173%.
Other Approaches:
- Use Market Data: Instead of deriving the forward rate from spot rates, you can use market data for FRAs and IRS to directly obtain pricing information.
- Sensitivity Analysis: Conduct sensitivity analysis by changing parameters like spot rates, FRA period, and spread to understand the impact on the fixed rate in the IRS.
