Pricing Eurodollar Futures and Hedging Commercial Paper Exposure
Summary
The document works through a hedge for a company planning to issue 180-day commercial paper. Because the company benefits from higher short-term rates when issuing the paper, it can short Eurodollar futures; the example scales the position by comparing the paper’s value and duration with those of the futures contract. The calculation gives an approximate contract count for the stated scenario.
It also explains the futures quote convention: the quoted price is 100 minus the annualized yield. A quote of 92 therefore represents an 8% annualized yield; applying that yield over the contract’s three-month deposit period gives a price of 98% of the contract notional, or $980,000 in the example. The hedge is an illustrative duration-based calculation, and the document does not explore basis risk, changing exposures, or other practical adjustments.
Key ideas
- Eurodollar futures quotes use a price convention of 100 minus the implied annualized yield.
- Convert the annualized yield to the contract’s three-month period to obtain its price as a percentage of notional.
- A company issuing commercial paper can short Eurodollar futures to hedge exposure to rising rates.
- The example scales the hedge by comparing the paper and futures values and durations.
Tags
Full text
# How does one calculate the Libor future contract price?
# How does one calculate the Libor future contract price?
I have the following question from Hull, problem 6.16:
Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue \$5 million of commercial paper with a maturity of 180 days. If the paper were issued today, the company would realize \$4,820,000. (In other words, the company would receive \$4,820,000 for its paper and have to redeem it at \$5,000,000 in 180 days’ time.) The September Eurodollar futures price is quoted as 92.00. How should the treasurer hedge the company’s exposure?
The solution is as follows:
The company treasurer can hedge the company’s exposure by shorting Eurodollar futures contracts. The Eurodollar futures position leads to a profit if rates rise and a loss if they fall. The duration of the commercial paper is twice that of the Eurodollar deposit underlying the Eurodollar futures contract. The contract price of a Eurodollar futures contract is 980,000. The number of contracts that should be shorted is, therefore:
$$\begin{align}Number\ of\ Contracts & =\frac{Portfolio\ Forward\ Value}{Future\ Contract\ Price}\times \frac{Portfolio\ Duration}{Futures\ Duration} \newline & =\frac{\$4\,820\,000}{\bbox[yellow, 5px,border:2px solid red]{$980\,000}}\times \frac{6\ months}{3 \ months} \newline &= 9.84\newline \therefore Number\ of\ Contracts &\approx 10\ \text{contracts}\end{align}$$
Question:
How does one calculate the future contract price of $980,000?
## Answer by Lliane (score 5, accepted)
https://quant.stackexchange.com/a/37111
The quoting convention must be explained somewhere in your book.
For Eurodollar futures, this convention is 100 - yield, 92 means the yield is 8% per annum, so for one quarter you need to divide this discount by 4 to get the price (100% - (8% × (3month/12month)) = 100% - 2% = 98%Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.