A 100 million interest rate swap has a remaining life of 10...

A $$\$ 100$$ million interest rate swap has a remaining life of 10 months. Under the terms of the swap, six-month LIBOR is exchanged for $4 \%$ per annum (compounded semiannually). Sixmonth LIBOR forward rates for all maturities are $3 \%$ (with semiannual compounding). The six-month LIBOR rate was $2.4 \%$ two months ago. OIS rates for all maturities are $2.7 \%$ with continuous compounding. What is the current value of the swap to the party paying floating? What is the value to the party paying fixed?

Key Concepts

Interest Rate Swap

An interest rate swap is a derivative contract in which two counterparties agree to exchange a series of cash flows over a specified period based on different interest rate structures. Typically, one leg of the swap involves fixed-rate payments, while the other involves floating-rate payments, such as those based on LIBOR. This contract is used for managing interest rate exposure and aligning cash flow profiles with an entity’s risk management strategy.

Fixed Leg and Floating Leg

The swap consists of two components: the fixed leg, where payments are made at a predetermined interest rate, and the floating leg, where payments vary based on an underlying index (e.g., LIBOR) that may change over time. The value of the swap depends on the present values of these two legs, and pricing involves aligning these cash flows to determine the swap’s net mark-to-market value for each counterparty.

Forward Interest Rates

Forward interest rates are the market’s expectations of future short-term interest rates and play a crucial role in pricing the floating leg of a swap. They are used to calculate the expected future cash flows that will be received or paid, thereby determining the present value of those cash flows under the risk-neutral pricing framework.

Discounting Cash Flows

Discounting is the process of determining the present value of future cash flows by applying an appropriate discount rate. In swap valuation, the discount factor reflects the time value of money and is often derived from market rates such as OIS rates or LIBOR-based discount curves. Selection of the discount rate can vary depending on the collateral and funding assumptions underlying the swap contracts.

Swap Valuation

Valuation of an interest rate swap involves calculating the difference between the present values of the fixed payments and the floating payments. The party receiving the cash flows with a higher present value holds a positive mark-to-market position. Accurate valuation requires careful consideration of payment schedules, compounding conventions, and the appropriate use of discount factors for each leg of the swap.

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