Introduction

Forward Rate Agreements (FRAs) play a crucial role in managing interest rate risk by allowing parties to lock in future interest rates. These agreements are widely used in financial markets to hedge against fluctuations in interest rates and to speculate on future rate movements. In this chapter, we will delve into the mechanics of valuing cash flows associated with Forward Rate Agreements and explore how they are calculated and applied in real-world scenarios.

Understanding Forward Rate Agreements (FRAs)

A Forward Rate Agreement is a contractual agreement between two parties to exchange interest rate payments on a notional amount over a specific period of time in the future. The key components of an FRA include the notional amount, the fixed interest rate (also known as the forward rate), the reference period, and the settlement date. The fixed interest rate is agreed upon at the inception of the contract and is used to determine the cash flows that will be exchanged at the settlement date.

Calculation of FRA Value

The valuation of an FRA involves determining the present value of the cash flows that will be exchanged at the settlement date. The cash flow received by the party receiving the fixed rate is calculated using the agreed-upon forward rate, the notional amount, and the length of the reference period. The cash flow received by the party receiving the floating rate is calculated based on the future spot rate prevailing at the settlement date.

The formula to calculate the value of an FRA for the party receiving the fixed rate is: $$ F R A_{\text {Fixed }}=\frac{N \times\left(R_{\text {FRA }}-R_{\text {Spot }}\right) \times \delta}{\left(1+R_{\text {Spat }} \times \delta\right)} $$ Where:

• $N$ is the notional amount
• $R_{\mathrm{FRA}}$ is the fixed interest rate agreed upon in the FRA
• $R_{\text {Spot }}$ is the spot rate for the reference period
• $\delta$ is the fraction of the year corresponding to the reference period Similarly, the value of the FRA for the party receiving the floating rate can be calculated by adjusting the formula accordingly.

Example: Let’s consider a scenario where Party A agrees to receive a fixed interest rate of 5% for a notional amount of USD 1,000,000 over a 3-month reference period, starting in 6 months. The current 3-month spot rate is 4.5%. We will calculate the value of this FRA for both parties.

For Party A (receiving fixed):
$$FRA_{\text{Fixed}} = \frac{1,000,000 \times (0.05 - 0.045) \times \frac{3}{12}}{(1 + 0.045 \times \frac{3}{12})} = USD 6,164.38$$

For Party B (receiving floating): $$FRA_{\text{Floating}} = \frac{1,000,000 \times (0.045 - 0.045) \times \frac{3}{12}}{(1 + 0.045 \times \frac{3}{12})} = USD 0$$