Introduction

In the world of swaps, understanding the valuation of plain vanilla interest rate swaps is crucial for both investors and financial professionals. This chapter delves into a method of valuing such swaps by considering two simultaneous bond positions. By dissecting the bond positions and their associated cash flows, we can unravel the value of the interest rate swap, offering a practical approach to valuation that is widely used in the financial industry.

Understanding the Valuation Method

Valuing a plain vanilla interest rate swap involves comprehending the underlying bond positions that make up the swap. The swap comprises two parties exchanging cash flows tied to fixed and floating interest rates. The value of the swap is determined by the difference between these cash flows. By analyzing the cash flows of both fixed-rate and floating-rate bonds, we can assess the swap’s value.

Step-by-Step Valuation Process

• Identify Bond Positions: Begin by identifying the fixed-rate bond and the floating-rate bond involved in the swap. Understand the coupon rates, face values, and maturities of these bonds.

• Calculate Fixed-Rate Bond Cash Flows: Compute the fixed-rate bond’s periodic coupon payments and its final principal repayment. These cash flows represent the outflows for the fixed-rate payer in the swap.

• Calculate Floating-Rate Bond Cash Flows: Determine the floating-rate bond’s interest payments based on the prevailing floating interest rate index. These cash flows mirror the variable payments that the floating-rate payer in the swap receives.

• Compare Cash Flows: Compare the cash flows from the fixed-rate and floating-rate bonds. Calculate the net cash flow difference between the two bond positions at each payment period.

• Calculate Swap Value: Sum up the present values of the net cash flow differences. The resulting value represents the theoretical value of the plain vanilla interest rate swap.

Example: Consider a plain vanilla interest rate swap where Party A pays a fixed 5% coupon and receives a floating rate based on the 3-month LIBOR from Party B. Party A holds a fixed-rate bond with a face value of USD 1,000,000 and a maturity of 5 years, while Party B holds a floating-rate bond with similar parameters. The current 3-month LIBOR is 4.25%.

• Party A’s fixed-rate bond cash flows: Annual coupon payment =$0.05 \times 1,000,000$ = USD 50,000; Final principal repayment = USD 1,000,000.

• Party B’s floating-rate bond cash flows: Quarterly interest payment = $\frac{0.0425}{4} \times 1,000,000 = 10,625$.

• Net cash flow difference: (50,000−10,625) = USD 39,375.

• Present value of net cash flow differences: Calculate the present value of USD 39,375 for each payment period and sum them up.

• The resulting sum is the value of the plain vanilla interest rate swap.