Introduction

In the realm of interest rate management and financial derivatives, Eurodollar futures play a crucial role in extending the LIBOR (London Interbank Offered Rate) zero curve. The LIBOR zero curve is a key tool for pricing and valuing various financial instruments, but it’s often limited by the available maturities of actual LIBOR rates. This chapter explores how Eurodollar futures can be effectively utilized to extend the LIBOR zero curve, providing financial professionals with enhanced tools for risk management and investment decision-making.

Understanding the LIBOR Zero Curve

The LIBOR zero curve is a graphical representation of the yields of various maturities of zero-coupon bonds, derived from LIBOR rates. However, LIBOR rates are typically available for a limited set of maturities, which can hinder precise pricing and hedging across a wider range of maturities. This is where Eurodollar futures come into play.

Role of Eurodollar Futures

Eurodollar futures are interest rate futures contracts that allow market participants to speculate on or hedge against future changes in short-term interest rates. These contracts are based on the future value of three-month LIBOR rates. Since Eurodollar futures are available for a range of maturities, they can be used to create synthetic LIBOR rates for different time periods, effectively extending the LIBOR zero curve.

Creating Synthetic LIBOR Rates

To extend the LIBOR zero curve, Eurodollar futures are used to create synthetic LIBOR rates for various maturities. The Eurodollar futures prices can be used to infer market expectations for future three-month LIBOR rates. By using a combination of Eurodollar futures contracts with different expirations, traders and investors can construct synthetic LIBOR rates for maturities that don’t have direct LIBOR rate quotes.

Example: Suppose the available LIBOR rates are only provided for maturities up to two years. To extend the curve to three years, a trader can use Eurodollar futures to create a synthetic three-year LIBOR rate. By analyzing the prices of Eurodollar futures contracts with different expirations, the trader can estimate the market’s expectations for the three-year LIBOR rate.

Calculation of Synthetic Rates

The formula to calculate the synthetic LIBOR rate for a specific maturity $n$ is:

$$\text {Synthetic LIBOR Rate}_n=\frac{100-\text {Futures Price}_n}{90-n}$$

Where:

• $\text{Futures Price}_n$ is the price of the Eurodollar futures contract for maturity $n$
• $n$ is the number of days until the maturity of the Eurodollar futures contract

Benefits and Considerations

Using Eurodollar futures to extend the LIBOR zero curve provides several benefits, including improved risk management, better pricing accuracy, and enhanced investment strategies. However, it’s essential to consider that Eurodollar futures are based on market expectations and may not precisely match actual future rates. Additionally, factors such as market volatility and liquidity should be taken into account when constructing synthetic rates.