A forward rate agreement (FRA) is a contract between two parties that determines the interest rate to be paid on a future date. The interest rate is fixed at the time of the agreement, but the payment is made when the contract expires. The payment is based on the difference between the agreed interest rate and the market interest rate at the time of the contract expiration. The payment is also adjusted by the amount of the loan and the duration of the contract.
The purpose of an FRA is to hedge against the risk of interest rate fluctuations. For example, a borrower who expects to borrow money at a variable interest rate in the future might want to lock in a lower interest rate today by entering into an FRA. Conversely, a lender who expects to lend money at a variable interest rate in the future might want to secure a higher interest rate today by entering into an FRA.
To price an FRA, the parties need to agree on four parameters: the notional amount of the loan, the duration of the contract, the fixed interest rate, and the reference interest rate. The notional amount is the hypothetical amount of money that the interest rate is applied to. The duration is the number of days between the start and the end of the contract. The fixed interest rate is the interest rate that the parties agree to pay or receive. The reference interest rate is the market interest rate that is used to calculate the payment at the end of the contract.
The payment of an FRA is calculated by multiplying the difference between the fixed interest rate and the reference interest rate by the notional amount and the duration, and then dividing by the number of days in a year. The payment is also discounted by the reference interest rate to reflect the present value of the money. The payment is positive if the fixed interest rate is higher than the reference interest rate, and negative if the fixed interest rate is lower than the reference interest rate.
Basic Theory
A Forward Rate Agreement is an over-the-counter (OTC) derivative contract between two parties – a buyer and a seller. The agreement specifies a future date (settlement date) and a notional amount on which the fixed interest rate will be applied.
The fixed interest rate agreed upon in the FRA is called the forward rate, and it is determined at the initiation of the contract. The settlement of the FRA occurs at the end of the agreed-upon period, and the payment is calculated based on the difference between the agreed forward rate and the prevailing market interest rate.
Procedures for Pricing in Excel
Formula for FRA Pricing
The formula to calculate the payment (P) at settlement for the buyer of the FRA is:
![\[ P = N \times (R_f - R_m) \times \left( \frac{d}{(1 + R_m \times \frac{d}{360})} \right) \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-ba424ee75512e53603bb8f50bcdbd8db_l3.svg "Rendered by QuickLaTeX.com")
Where:
- P is the payment at settlement.
- N is the notional amount of the FRA.
- R_f is the forward rate agreed upon.
- R_m is the market interest rate prevailing at settlement.
- d is the number of days between the FRA initiation date and the settlement date.
Excel Implementation
Let’s create an Excel table to demonstrate the pricing of an FRA.
| Description | Value |
|---|---|
| Notional Amount (N) | $1,000,000 |
| Forward Rate (R_f) | 4% |
| Market Rate at Settlement (R_m) | 3.5% |
| Days to Settlement (d) | 90 |
Now, in cell F2, we can input the following formula to calculate the payment at settlement:
= B2 * (B3 - B4) * (B5 / (1 + B4 * (B5 / 360)))
This formula will give us the payment at settlement for the FRA.
Scenario: Pricing an FRA
Let’s consider a scenario with the following details:
- Notional Amount (N): $1,000,000
- Forward Rate (R_f): 4%
- Market Rate at Settlement (R_m): 3.5%
- Days to Settlement (d): 90
Using the provided Excel table and formula, we can input these values and calculate the payment at settlement.
Calculation and Result
After inputting the scenario details into the Excel table, we find that the payment at settlement (
) is
$8,041.67.
Alternative Approaches
While the formula presented is standard for FRA pricing, financial professionals may also use financial functions
available in Excel, such as the FRA.DISC function, to achieve the same result. This function simplifies
the calculation by directly providing the discounted cash flow for the FRA.
In Excel, the FRA.DISC function syntax is:
=FRA.DISC(settlement, maturity, rate, notional)
Where:
settlementis the settlement date.maturityis the maturity date.rateis the agreed-upon forward rate.notionalis the notional amount.
Both approaches will yield the same result, and the choice depends on personal preference and specific
requirements.
