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Topic Title: Bootstrapping zero coupon curve from deposit futures and swap rates
Created On Wed Jul 16, 03 09:55 AM
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Bazman
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Wed Jul 16, 03 09:55 AM
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Hi,

I am currently implementing a procedure to bootstrap the zero curve from deposit, futures and swap rates. The technique is rather simple relying on a genetic agorithm to fit the 3m forwards curve that is consistent with all the underlying instuments (as far as possible). I was fitting fot 3month forward out 20 years and while the results were excellent the method is chronically slow.

I was just wonderinf if anyone knows of any other techniques to fit the zero coupon curve to the above instruments, which is quick and preferably sacrifices as little as possible in terms of accuracy.

Baz

Edited: Wed Jul 16, 03 at 09:58 AM by Bazman
 
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FDAXHunter
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Wed Jul 16, 03 10:02 AM
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Errm, why are you using a GA to do that? You can solve for it analytically? If you do a GA, you are most likely going to violate no-arbitrage restrictions.

A GA could not possibly be more accurate than a analytic bootstrap, but maybe you are talking about something else?

Regards.

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Chiral3, kr, Nonius, Newton and FDAXHunter on a little boat drifting aimlessly on Hell's vast lake of burning sulphur.
 
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Bazman
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Wed Jul 16, 03 10:35 AM
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Hi,

Well it was no-arbitrage that was my primary concern. I thought becasue the deposits and futures overlap at the short end and also the futures and swaps overlap at the long end, it is difficult to get a bootstrap that is consistent with them all. if you simply remove the overlaps and bootsprap you will be arbitrage free but the you will be left with a higly irregular forward curve which is obviously not good either!
 
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FDAXHunter
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Wed Jul 16, 03 10:37 AM
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You are aware of the convexity bias in the futures, yes?

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Chiral3, kr, Nonius, Newton and FDAXHunter on a little boat drifting aimlessly on Hell's vast lake of burning sulphur.
 
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Bazman
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Wed Jul 16, 03 11:21 AM
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No I have to admit I'm not sure what you mean here. I'm familiar with the concept of concept of convexity. in terms of bonds. But have not really considered it here.

How would I calculate the convexity on the futures?

And how would this affect the smoothing of the curve? Surely the problem of switching between different instuments will remain???

Baz
 
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FDAXHunter
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Wed Jul 16, 03 11:41 AM
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No, the problem won't remain, because if you are adjusting the futures for convexity, then they will line up more or less with swaps (otherwise there will be an arb).

To adjust for the convexity on the futures, you lower their price (increase the forward rate).

You can calculate the Bias like this:

Bias = Vol(ForwardRate)*Vol(ZeroRate)*Correlation(ForwardRate, ZeroRate)

Here's the current Convexity bias structure for Eurodollar futures.

Fut (bps)
EDU3 0.52
EDZ3 0.00
EDH4 0.00
EDM4 0.00
EDU4 0.26
EDZ4 1.04
EDH5 2.16
EDM5 3.62
EDU5 5.25
EDZ5 6.88
EDH6 8.52
EDM6 10.15
EDU6 11.79
EDZ6 13.44
EDH7 15.08
EDM7 16.73
EDU7 18.45
EDZ7 20.32
EDH8 22.33
EDM8 24.49
EDU8 26.79
EDZ8 29.23
EDH9 31.82
EDM9 34.56
EDU9 37.31
EDZ9 39.95
EDH0 42.48
EDM0 44.91

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Chiral3, kr, Nonius, Newton and FDAXHunter on a little boat drifting aimlessly on Hell's vast lake of burning sulphur.
 
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Bazman
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Wed Jul 16, 03 01:02 PM
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Hi,

Thanks for all your help its much appreciated.

Just wondering though where do you get the vols from? Are those quoted?

If not I guess I could calculate the vol on each quoted contract using say historical closes going one month back?? (is that reasonable)

And I could do the same for quoted zero coupon rates and work out the correlation.

Any recommendations for could reuters/bloomberg pages with good zero coupon rate quotes?

Just to be clear if I then add these and just bootstrap the analytic way solving one discount factor after the other I should get a smothe curve?

Baz
 
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FDAXHunter
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Wed Jul 16, 03 01:08 PM
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You get the vols from the Eurodollar options or from swaptions and caps/floors.

Using historical vol is not reasonable, you're curve will be not in line with the market. However, the convexity bias structure doesn't change that much, so it's not like you need to update every hour. There are many banks who provide this free of charge. Ask your favorite dealer (who do you work for? Don't they have a swap desk?)

Yes, you should get a smooth curve. Except , maybe in the first month.

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Chiral3, kr, Nonius, Newton and FDAXHunter on a little boat drifting aimlessly on Hell's vast lake of burning sulphur.
 
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Slewfoot
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Wed Jul 16, 03 03:18 PM
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Bloomberg has a function FWCV that bootstraps a zero from IRSB inputs. FWCV <go> then tab to change from coupon to spot. But I haven't found it to be too accurate. We just bought the Swapmaker data which is Cantor Treasury quotes and Tullett swap spreads then boostrapped in Excel with manual futures inputs. That was good enough for the simple trades we do.
 
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Bazman
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Thu Jul 17, 03 09:33 AM
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Hi Tnx Again FDAXHunter,

We are a new oil trading company, but will be using swaps for hedging.

Just trying to set up our own pricing sheets, obviously though if I can calculate the convexity myself so much the better. (Makes sense not to rely on my broker for info to drive our internal pricing models.)

Therefore I don't really have a desk I can go to at present. I will have a look at calculating the bias today. If its just a case of taking the vols and applying them to the equation with no further adjustments should be reasonably straighforward.(fingers crossed).

Baz
 
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Bazman
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Thu Jul 17, 03 09:38 AM
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Hi Slewfoot,

How do you mean "then boostrapped in Excel with manual futures inputs". Do you mean you just fitted to the deposit treasury and swap quotes?

Baz
 
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FDAXHunter
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Don't you have a Bloomberg or Reuters or something? You can also get FinCAD, which does all this shit for you.

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Chiral3, kr, Nonius, Newton and FDAXHunter on a little boat drifting aimlessly on Hell's vast lake of burning sulphur.
 
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Bazman
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Thu Jul 17, 03 11:10 AM
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Hi ,

Yeah I have access to all 3 but I'd rather rely on my own calculations as slewfoot pointed out the Bloomberg is not often that accurate and I've not got much faith in Reuters. Its so simple conceptually but has proven quite problematic to implement.

My last point on this and correct me if I'm wrong but if you do use the convexity correction to bring the futures into line witht he swaps. Surely there you are probably just as well just fitting to the depoist and swap rates which is alot easier to implement?

Baz
 
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FDAXHunter
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Thu Jul 17, 03 12:05 PM
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The swaps have to be inline with the Eurodollars, otherwise there is an arb (ask andym, he gets on the wrong side of it all the time... hehe).

You can of course also fit only to deposit rates and swap rates. Just remember that Eurodollar futures are the supreme instrument for price discovery as far as the forward curve goes (well, out to the golds anyway).

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Chiral3, kr, Nonius, Newton and FDAXHunter on a little boat drifting aimlessly on Hell's vast lake of burning sulphur.
 
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DavidJN
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Thu Jul 17, 03 01:44 PM
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Notice from FDAXHunter?s posting of the empirical convexity bias for Eurodollar futures how the bias grows exponentially with the maturity of the contract. The front four contracts display virtually no bias. So, if you use only the front four, followed by swap quotations, you can avoid the necessity of correcting convexity bias altogether. You may safely assume that the swap quotations have already done this for you.

In Canada we generally use only the front four BAX (our erquivalent of Eurodollar) contracts because there is NO liquidity after that point anyway. This of course begs the question - how are Canadian swap dealers arriving at short-dated swao quotations?
 
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elan
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Thu Jul 17, 03 01:46 PM
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BTW, beware of naive bootstrapping algorithm (no matter how carefully you select your input benchmark instruments): your forwards will be badly screwed up. A partial list of non-starters: linear interpolation of forwards, linear interpolation of swap rates, linear interpolation of discount factors, ...

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Bazman
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Thu Jul 17, 03 03:53 PM
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hi,

BTW am now using the following page on Bloomberg: EDS. To get the Bias.

However the rates are pretty different to those quoted by FDAX Hunter. FADX have the bias's moved significantly (I'm aware you siad this was unlikely) or is it just the case that these Bloomberg figures are unreliable?

Please let me know what you think.

EDU3 0.08
EDZ3 0.27
EDH4 0.55
EDM4 0.91
EDU4 1.36
EDZ4 1.88
EDH5 2.49
EDM5 3.22
EDU5 3.98
EDZ5 4.75


 
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FDAXJihad
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Thu Jul 17, 03 04:55 PM
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I believe Bloomberg uses slightly different method to getting their bias. The ones I gave you come from caps/floors quotes.

Bloomberg probably uses something much simpler.

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Yallah!!!
 
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Slewfoot
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Thu Jul 17, 03 05:20 PM
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Quote

Originally posted by: Bazman
Hi Slewfoot,

How do you mean "then boostrapped in Excel with manual futures inputs". Do you mean you just fitted to the deposit treasury and swap quotes?

Baz


Right, calculated the forward rates & then discount rates. Used .5 year intervals. We don't need extreme accuracy but traders were promising L+ spread and we were getting L + spread - 4 or 5 bps.

Note elan's warning re interpolations, though.
 
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elan
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Thu Jul 17, 03 06:50 PM
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Quote

Originally posted by: FDAXJihad

Bloomberg probably uses something much simpler.


Whatever they do, their convexity adjustments are decent.


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