SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
awc
Topic Author
Posts: 6
Joined: April 18th, 2017, 3:13 pm

OIS Pay lags and discount factors

April 18th, 2017, 4:38 pm

Hi, I've been getting myself in a muddle in deriving discount factors from OIS curves and would be grateful for any pointers.

I think my problem boils down to: "When deriving the discount factor/zero rate from a par OIS rate do you include the pay lag?" but I've left an example (that I derived from bloomberg) below.

For example from Bloomberg
The 2W USD OIS swap;
 Effective 20-Apr-17
 Maturity 04-May-17   (14 Actual days from Effective date)
 Payment 08-May-2017 (18 Actual days from Effective date, +2 pay lag from maturity)
 Coupon: 89 basis points

If I use this rate to make a discount factor, am I getting the discount factor to the 4th or 8th May?
If it's the 4th May then, the zero rate is the same as the par rate around 0.89
If it's the 8th May then, the extra two days makes the zero rate around 62bps which is what bloomberg gives for the zero coupon price and the discount factor

As it's paid on the 8th I understand if it would be to the 8th may but I don't get the fundamentals behind how a zero rate of 62 basis points makes any sense when effective fed funds is >90 and is expected to increase? Wouldn't that additional compensation for the pay lag been included in the price?

I appreciate that this is really only a material problem with the front end as the pay lag is a greater proportion of it there but it's been doing my head in for a while so I'd be grateful for anything that can settle this.

Thanks, AWC
 
User avatar
mtsm
Posts: 327
Joined: July 28th, 2010, 1:40 pm

Re: OIS Pay lags and discount factors

April 19th, 2017, 4:11 am

Do you have the CS Basis Points doc from 2010?
 
awc
Topic Author
Posts: 6
Joined: April 18th, 2017, 3:13 pm

Re: OIS Pay lags and discount factors

April 19th, 2017, 8:45 am

The one titled "A Guide to the Front-End and Basis Swap Markets"? Thanks, I hadn't but I just took a look, unfortunately it doesn't help with the mechanics of dealing with days/pay lags.
 
User avatar
mtsm
Posts: 327
Joined: July 28th, 2010, 1:40 pm

Re: OIS Pay lags and discount factors

April 19th, 2017, 2:43 pm

Yes it does, look at the simple example. And write to BBG - get help from a BBG meta-meta-helper who will put you in touch with a meta-helper who will call for help form a helper who will help you. Ask them what they do and why.

The pay-lag exists because of the delayed publication of the fixing. Not sure why you want to use it to compute anything. The instrument in your example ends on the 4th, not the 8th. 
 
awc
Topic Author
Posts: 6
Joined: April 18th, 2017, 3:13 pm

Re: OIS Pay lags and discount factors

April 19th, 2017, 3:12 pm

That's the essence of my question which unfortunately bbg couldn't help with the why.

They include the pay lag in the daycount for the discount factor/zero rate calculation; i.e. their discount factor for the 8th is the instrument maturing on the 4th, so the zero rate goes down to 61 bps (so less than the effective fed fund rate).

I'm of two minds, my first instinct was the same as you; why would you include the lag.
But thinking about it from a no arbitrage standpoint, shouldn't you be able to roll a repo from the swap start to PAYment date and have no arbitrage (assuming no change in repo rates).
 
User avatar
Magnyz
Posts: 63
Joined: July 14th, 2002, 3:00 am

Re: OIS Pay lags and discount factors

April 19th, 2017, 3:47 pm

In my opinion the discount factor you derive is for the day you have the cashflows i.e. it includes the payment lag. In your example the point on the discount function you derive is the 8th. The 4th is just a "calculation day".
 
User avatar
mtsm
Posts: 327
Joined: July 28th, 2010, 1:40 pm

Re: OIS Pay lags and discount factors

April 20th, 2017, 12:58 am

I am not really sure where the confusion is. 

What BBG functionality are you referring to? ICVS 42? Maybe what thety do is right and you are misinterpreting what they do.

Maybe if you highlight what you mean by "deriving the discount factor from the par OIS rate", it will become clear. Can you be more explicit?
 
User avatar
Magnyz
Posts: 63
Joined: July 14th, 2002, 3:00 am

Re: OIS Pay lags and discount factors

April 20th, 2017, 5:34 am

It seems pretty clear to me. Do you get a discount factor on the 4th or on the 8th in the example above?
 
User avatar
mtsm
Posts: 327
Joined: July 28th, 2010, 1:40 pm

Re: OIS Pay lags and discount factors

April 20th, 2017, 1:02 pm

Between 4/20 and 5/4, hence to the 4th.
 
User avatar
Magnyz
Posts: 63
Joined: July 14th, 2002, 3:00 am

Re: OIS Pay lags and discount factors

April 20th, 2017, 1:14 pm

Cashflow is paid on 5/8, hence to the 8th. ;-) 
 
User avatar
mtsm
Posts: 327
Joined: July 28th, 2010, 1:40 pm

Re: OIS Pay lags and discount factors

April 20th, 2017, 1:26 pm

I don't copy that, but may easily be wrong about that, I no longer work in that asset class. But let me spell out what I think. I think the OP was not being very lucid.

So the instrument goes strictly between 4/20 and 5/4. The 5/8 is for practical purposes only. There isn't any rate accruing beyond 5/4. If you know the OIS fixed rate between 4/20 and 5/4, you can compute the accrued interest between these two dates or vice versa back out a discount. That's all there is to it, it doesn't matter whether the payout is on the 8th.

I am not sure if the OP is confused or not, but it sounds like the only way to get a significantly smaller par rate, would be to compound the the floating leg between 4/20 and 5/4, but have the fixed run between 4/20 and 5/8. Given the floating fixings, you can back out the par rate this way and the extra 4 days accrual on the fixed side would account for a larger day count fraction, which would explain why the OP got the smaller rate. 
 
User avatar
Magnyz
Posts: 63
Joined: July 14th, 2002, 3:00 am

Re: OIS Pay lags and discount factors

April 20th, 2017, 2:18 pm

Well, I can be wrong as well but in my mind when you want to back out the discount factor it is the day when you have the actual cashflows that are important (regardless of accrual or not). As a thought experiment ... assume you have one usd ois swap without paylag and another with a 1month paylag, would you quote the same price?  
 
awc
Topic Author
Posts: 6
Joined: April 18th, 2017, 3:13 pm

Re: OIS Pay lags and discount factors

April 20th, 2017, 2:53 pm

For me, what matters for setting the amount paid is obviously the dates you accrue but as you paid later surely you need to get compensated extra for those two days?

MTSM, regarding your earlier point. I did look at ICVS but that didn't help too much, the stripped curve part of that screen shows payment dates rather than maturity dates. What I've been using is the Bloomberg Curves toolkit in Excel. I've been stripping the curve as   A1 = Bcurvestrip("USD.OIS") and then getting zero coupon mids and discount factors using

bcurveint(A1,"ZC.MID",DATE)
bcurveint(A1,"DF.MID",DATE)

Putting in all good dates within the next month, you get rates lower than 91 basis points, even as low as 62bp. Hence, my confusion which is lines up with Maynyz's "thought experiment".

I think part of the issue is that the USD.OIS curve doesn't necessary use the same compounding and frequencies as the swaps but I struggle to see how it would have that big of an effect.
 
User avatar
mtsm
Posts: 327
Joined: July 28th, 2010, 1:40 pm

Re: OIS Pay lags and discount factors

April 21st, 2017, 2:21 am

In order to recover (reprice) the OIS par rate, you need to actually price up the floating leg. In case you are just requesting a discount factor from the curve end then expect the zero rate to be close to the OIS rate, that's not right. The reason is that you neglect compounding. I don't think this is related to the pay lag.

Try the following. Request a daily series of discount factors from your curve, then compute one-day forward discount factors, then back out one-day forwards. Do this for every day in between effective and maturity. Now, compute the floating leg by the compound interest accrued over the length of the leg, and then normalize this by the fixed leg day count fraction ACT360. This should result in the input rate. I am just spelling out the computation found in the note I referred you to.    
 
User avatar
BerndSchmitz
Posts: 232
Joined: August 16th, 2011, 9:48 am

Re: OIS Pay lags and discount factors

April 26th, 2017, 12:44 pm

ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...