Deriving Zero-Coupon Rates from Eurodollar Futures

Summary

The document explains how to interpret Eurodollar futures prices as implied forward rates and use them to build a sequence of zero-coupon rates and discount factors. Its central step is to convert each quoted futures price into a rate by subtracting the price from 100. Each contract then represents a forward rate for its accrual period, and the rates can be chained from a starting date to later maturities.

The examples show several contract prices alongside purported zero rates and discount factors, but the text does not derive those figures or provide enough conventions to reproduce them. It says a short initial spot LIBOR rate is also needed to connect today to the first futures period, and that discount factors follow from the resulting zero rates. The explanation is introductory: it does not discuss day-count rules, compounding conventions, convexity adjustments between futures and forwards, or how to handle contract-specific dates. Those details matter for precise curve construction.

Key ideas

• A Eurodollar futures quote is converted to an implied rate by subtracting its price from 100.
• Each contract supplies a forward rate for a period between contract dates.
• Zero-coupon rates for later dates are built by chaining the initial spot rate and intervening forward rates.
• Discount factors are then derived from zero rates using the selected compounding convention.
• The examples do not specify the conventions needed to reproduce the displayed curve values.

Tags

# Calculating the interest rate from a EuroDollar Futues contract


# Calculating the interest rate from a EuroDollar Futues contract












I would like to calculate the interest rate from a EuroDollar Future Contract(say the Sep-16 Futures Contract is trading at 99.2575). From the interest rate, I would like to calculate the zero coupon rate and discount factor.

The values of EuroDollar Futures Contract looks like this:

```
        Price   Zero Coupon Discount Factor
Sep-16  99.2575 0.673049123 0.997116025
Dec-16  99.185  0.725403393 0.995093125
Mar-17  99.1475 0.757944554 0.993081443
Jun-17  99.1075 0.787513853 0.990695774
```

Not sure how to work out the interest rate, zero coupon and discount factor.

Need some guidance on doing this.

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/28218

1) convert the futures prices into forward rates by using forward rate= 100- futures price. You now have a chain of forward rates, starting with the rate from Sep 16 to Dec 16.

2) you need a rate from today to Sep 16. Use 2 month spot Libor

3) to calculate a zero coupon rate from today to any given date, chain together the relevant forward rates. eg the rate to Mar 17 is calculated by chaining together (today to Sep16), (sep 16 to dec 16), (dec 16 to mar 17).

4) discount factors can be calculated from zero coupon rates in the standard manner (reciprocal of one dollar invested in the zero coupon rate for the relevant period)

## Answer by mbison (score 0)

https://quant.stackexchange.com/a/28216

these instruments are quoted as: 100 - yield. Thus 99.25 would correspond to a yield of 0.75 (%).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.