Anyone understand Eurodollar future pricing (LOS 61g)?

willispierre

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I understand that it is priced at a discount yield (unlike t-bills). But the explanation from there in both schweser and CFAI are a little unclear.
Anyone have a 2-3 sentence explanation of why arbitrage is not possible (and therefore pricing is difficult)
 
I competely agree with you, found exactly the same. Would be interested in hearing any comments.
 
First, LIBOR is an add on rate. Second, we won’t know the LIBOR rate ahead of time (like we know for T-Bills). So if you look at Schweser’s section, it has that funky equation. There is that LIBOR rate in the denominator, that’s the one that we can’t determine ahead of time. That’s why you can’t have perfect arbitrage free pricing based on LIBOR rates (but people use approximation anyways).
 
If a 3 month Euro Dollar future is trading at 97, that means that your yield is 3% x (3/12). So you subtract the price from 100 and adjust for the time period.
 
sebrock - that much i unserstand….. eltia - this pretty much mimics schweser, but I still don’t get it. how do you know what t-bill rate will be anymore than LIBOR? You can use off-the-run issues in order to arbitrage?
 
http://www.analystforum.com/phorums/read.php?12,926972,927044#msg-927044
Pasted stuff from there for you:
Tbill Pricing
For some wierd historical reason and to make our life miserable, T-Bill is quoted differently from its price - meaning its quote is not its price. It is quoted at annualized discount. So adjust accordingly. So if quoted at 4% annulaized discount, the price is really (1-.04*90/360) i.e .99 So you pay .99 and get 1 when it expires. The yield (r) for 90 days is (1-.99)/.99 .
Futures pricing
Remember two things. Firstly, good old formula Future price, F= S*(1+r)**T. where r = risk free rate and T is expiration Time of future. Secondly, note (usual tripping point), there are two expiration days here 1) expiration of future and 2)expiration of underlying. The T above is expiration of future. the underlying is typically a 90 day instrument but it could be any h day T-bill.
Step 1 Get S
To get future price of n days on a 90 day underlying from you will need a T-bills greater than n days i.e n+90 days. If the future is for a h day (instead of 90 day) instrument then the you need T-bill expiring in n+h days. Anyway once you have this, use above Tbill pricing formula to get the spot price. So from CFAI text
140 day bill trading at 4.6% discount is 1 - .046*140/360=.9821
Step 2 Get (1+r)**T;
r is the risk free rate. So the (1+r)**T can also be looked at the yield on a T-bill for n days. So get the yield on a second T Bill expiring in n days. This corresponds to expiration days of t-bill Future. Assuming 50 day tbill is at 5% discount , price is 1-.05*50/360 =.9931. So (1+r)**T is equal to 100/.9931.
Step 3
Future Price = Step 1* Step 2. Note you have computed future price for a future expiring in 50 days for 140-50 i.e 90 day underlying T-bill.
Valuation
Actual futures values are not so painful as forwards as they are exchange traded and marked to market dialy - so one does not have to worry about value. Their value at end of each day is 0.
Eurodollars
They are priced like as T-bills future. This is not to confuse traders who were used to the T-Bill quotes. But that is not how Eurodollars time deposits are executed in practice. The interest is a add on yield . So a $1 Eurodollar time deposit is not priced at less than 1. It is priced at $1 and after n day you you get (1+r*90/360). A T-bill would be priced at (1-r*90/360) and executed thus in practice too. So the (1+r)**T in eurodollar Future does not match yield in practice. Hence the problem.
 
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