Introduction

In the realm of interest rate futures, the Eurodollar futures contract holds a significant position. While it serves as a tool for managing interest rate risk, its accuracy can be enhanced through the concept of convexity adjustment. Convexity adjustment takes into account the non-linear relationship between interest rates and bond prices, offering a more precise valuation. This chapter delves into the concept of Eurodollar futures contract convexity adjustment, its importance, and how to compute it effectively.

Understanding Convexity Adjustment

The convexity adjustment arises due to the curvature in the relationship between interest rates and bond prices. As interest rates change, the impact on bond prices isn’t perfectly linear. Convexity captures the curvature in this relationship. In the context of Eurodollar futures, the convexity adjustment accounts for the effect of changes in the forward rate curve on the contract’s value.

The convexity adjustment (CA) can be calculated using the formula:

$$CA=\frac{1}{2} \times \text{Convexity} \times(\Delta r)^2 \times \text{Contract Notional}$$ Where:

• Convexity is the bond’s convexity measure.
• $\Delta r$ is the change in interest rates.
• Contract Notional is the notional value of the Eurodollar futures contract.

Example: Let’s consider a Eurodollar futures contract with a notional value of USD 1,000,000 and a convexity of 100. If the interest rates change by 0.01 (1%), the convexity adjustment can be calculated as follows:

$$CA = \frac{1}{2} \times 100 \times (0.01)^2 \times 1,000,000 = \text{ USD 5,000}$$

In this scenario, the convexity adjustment accounts for the curvature in the relationship between interest rates and the contract’s value.

Significance of Convexity Adjustment

The convexity adjustment is crucial for accurately valuing Eurodollar futures contracts, especially when interest rate changes are significant. By incorporating the non-linear effects of interest rate movements, traders and investors can make more informed decisions regarding hedging strategies and risk management.