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# Eurodollar Futures.

#### PaulGrey

##### New Member
Hi David,

Sorry, but I’ve got another question if you’ve got some spare time, this time relating to Eurodollar futures. No urgency though, it’s more curiosity than anything else.

When pricing a future we have a combination of equations depending on the underlying which results in a combination of slightly different pricing equations of something in the form of F=So.e^rt …… nice and easy….

Now when we price a Eurodollar Future we use the formula.
F = 10,000[100 - 0.25(100-Q)]

I was a bit curious about this formula and why it is so, I reworked it slightly to get:
F=1000000[1 – 90/360 (1-q/100)) or
F=1000000[1 – 0.25 (1-q/100)) where I think the (1-q/100) part converts a quote of say 98 to 2% ….. i.e. (1-98/100) = (1-0.98) = 2%

So the way I’m looking at it, is that the futures price is actually the discount of the principle, multiplied by the Eurodollar interest rate converted to 3 months (90/360). Or in other words the discount of the principle due to the cost of money for 3 months.

So assuming that is correct, I finally get to my questions: is this effectively just looking at a future 3 months Eurodollar interest rate which is what is used to define the quote price? And also since the Eurodollar is the rate banks borrow to each other, what are the differences between the Eurodollar and LIBOR – are they interchangeable?

Thanks,
Paul

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Paul,

That's interesting. I'll admit I get a little confused with Hull's use of phrase "Eurodollar interest rate."

You can see in the specs the ED is a futures contract on LIBOR. (the "Eurodollar" is just a dollar deposit somewhere outside the US). So, I *personally* have a hard time thinking of it as a "rate" per se; it's an exhange-traded contract built around LIBOR. Just a contract that trades, it doesn't really price an asset, and it doesn't quite converge to face (it converges to, as implied in your formula: 100 - 3 month LIBOR/4). So, when you say "the futures price is actually the discount of the principle..." I basically agree with that except there is no principal, only a notional. The contract is pricing the LIBOR as a discount rate (like you could, if you switched from regular convention, say the price of a zero coupon bond = 100 - (rate)(100)(days/year). That would be an okay way to talk about bond yields, except by convention nobody does). This ED pricing is essentiallly a discount rate (i.e., the contract prices a forward LIBOR by using a discount rate method) but, unlike a bond that would be converging to 100 face, the ED contract is converging to 100 - libor/4.

But i have an easier time just seeing as a construct of the CME - a forward on LIBOR - not as having other fundamental qualities. (And, i may need to be corrected, but that's why i have a hard time thinking about a "Eurodollar rate" as anything other than a byproduct of the CME construct and not linking to anything intrinsically except forward LIBOR.) The pricing formula, it may help to know, was designed so that a 1 bsp change = $25; i.e., they could have specified a different contract price! You'll notice your formula has a simpler reduction, since 100 - Q = q (e..g, 100 - 98 = 2), F = 10,000[100 - 0.25q] = 1 million - 2,500q. e.g., if Q = 98, then q= 2, and F = 1 MM - 5K = 995,000. Thanks, David #### jonnynewxs ##### New Member Hello just chanced upon the forum while searching info on interest rate futures, Just a quick question concerning the pricing formula of the eurodollar futures. As mentionned in the previous post the price is the discounted value of the principle. However the rate used to discount is a LIBOR rate. Why is the formula 100-.25*q? And not 100/(1+.25*q). Many thanks in advance, Jon #### shivanin ##### Member Subscriber Hi Paul, That's interesting. I'll admit I get a little confused with Hull's use of phrase "Eurodollar interest rate." I think the actual contract specs are helpful: http://www.cme.com/trading/prd/ir/eurodollar_FA.html . You can see in the specs the ED is a futures contract on LIBOR. (the "Eurodollar" is just a dollar deposit somewhere outside the US). So, I *personally* have a hard time thinking of it as a "rate" per se; it's an exhange-traded contract built around LIBOR. Just a contract that trades, it doesn't really price an asset, and it doesn't quite converge to face (it converges to, as implied in your formula: 100 - 3 month LIBOR/4). So, when you say "the futures price is actually the discount of the principle..." I basically agree with that except there is no principal, only a notional. The contract is pricing the LIBOR as a discount rate (like you could, if you switched from regular convention, say the price of a zero coupon bond = 100 - (rate)(100)(days/year). That would be an okay way to talk about bond yields, except by convention nobody does). This ED pricing is essentiallly a discount rate (i.e., the contract prices a forward LIBOR by using a discount rate method) but, unlike a bond that would be converging to 100 face, the ED contract is converging to 100 - libor/4. But i have an easier time just seeing as a construct of the CME - a forward on LIBOR - not as having other fundamental qualities. (And, i may need to be corrected, but that's why i have a hard time thinking about a "Eurodollar rate" as anything other than a byproduct of the CME construct and not linking to anything intrinsically except forward LIBOR.) The pricing formula, it may help to know, was designed so that a 1 bsp change =$25; i.e., they could have specified a different contract price!

You'll notice your formula has a simpler reduction, since 100 - Q = q (e..g, 100 - 98 = 2),
F = 10,000[100 - 0.25q] = 1 million - 2,500q.
e.g., if Q = 98, then q= 2, and F = 1 MM - 5K = 995,000.

Thanks, David
Hi David,
In this formula why do we do10,000( 100 - 0.25q) ? ....i.e. why we subtract 0.25q from 100 ??
Unable to understand this formula.

Thanks a lot.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @shivanin The ED futures contract price = 10,000 * [100 - 0.25*(100 - Q)] per Hull 6.2, or since Libor, R*100 = 100 - Q, we could also say the contract price = 10,000 * [100 - 0.25*L*100)]. The way i think about this is, imagine there was no 0.25, then this would be simple:
• price = 10000*[100 - (100 - Q)] = 10,000*Q. This would be the design for a contract price that would change $100.00 in value for every one basis point change in the rate. There is nothing magic about the 10,000 except that is scales the contract to a nominal value of$1.0 million as a convenient trading unit. So for example, if LIBOR increased by one basis point from 1.00% to 1.01%, the price of this "as if" contract would be 10,000*98.990 = $989,900 which would represent a$100 drop in the contract price. I am taking out the 0.25 temporarily only to highlight how this formula is effectively just multiplying the quote, Q (e.g., 98.990) which is just the inverse of the rate (Libor = 1.01%). Directionally, the ED futures contract is like a bond: when the rate, L, goes down, the quote goes up per Q = 100 - L. In this way, the [100 - (100 - Q)] is a way of setting up an inverse relationship (similar to bonds) between rates and price (after all, they could have designed a contract whose price went up when rates go up, but they didn't ...) and then the 10,000 multiplier is a somewhat arbitrary scaling to $1.0 mm face value • Then the 0.25 is because the rates are expressed per annum but the it's a three-month LIBOR and, as Hull explains, the design is such that a one basis point change in the LIBOR is meant to correspond to a$25.00 change in price. I suppose this could be viewed as arbitrary but it makes sense given it's a three month rate, I think. I hope that helps!

#### shivanin

##### Member
Subscriber
Thanks a lot for this explanation David.