Introduction

Understanding the computation of discount rates in a plain vanilla interest rate swap is crucial to grasp the fundamental mechanics of this financial instrument. Discount rates play a pivotal role in determining the present value of future cash flows exchanged between parties in a swap agreement. In this chapter, we will delve into the intricacies of how these discount rates are derived and applied in the context of a plain vanilla interest rate swap.

Determining the Fixed and Floating Rates

Before we delve into discount rate computation, it’s essential to establish the fixed and floating rates in a plain vanilla interest rate swap. The fixed rate is predetermined at the initiation of the swap and remains constant over the life of the agreement. The floating rate, on the other hand, is often linked to a reference rate, such as LIBOR, and resets periodically based on market conditions.

Calculation of Present Value Factors

The present value factors are integral to determining the discount rates in a plain vanilla interest rate swap. These factors consider the time value of money and convert future cash flows into their equivalent present values. The formula for calculating the present value factor for a particular period can be represented as:

$$PVF_n=\frac{1}{(1+r)^n}$$

Where:

• $P V F_n$ is the present value factor for period $n$,
• $r$ is the discount rate, and
• $n$ is the period.

Implied Forward Rates

Implied forward rates are an essential component of discount rate computation in swaps. These rates reflect the market’s expectations for future interest rates. In a plain vanilla interest rate swap, the fixed rate is derived from the series of implied forward rates, ensuring that the present value of fixed rate payments matches that of floating rate payments over the life of the swap.

Determining the Discount Rate

The discount rate used in a plain vanilla interest rate swap is the rate that, when applied to the future cash flows, results in the present value of the fixed rate payments equaling the present value of the floating rate payments. This rate is determined iteratively by adjusting the fixed rate until the present value equality is achieved.

Example: Let’s consider a hypothetical plain vanilla interest rate swap between Company A and Company B. Company A agrees to pay a fixed rate of 4% while receiving LIBOR + 2%. The swap has a notional value of $1,000,000 and a maturity of 5 years. Implied forward rates for the next five years are 3.5%, 4.0%, 4.2%, 4.8%, and 5.5%. By iteratively adjusting the fixed rate, we can calculate the discount rate that equalizes the present values of fixed and floating rate payments.