Swap valuation with eurodollar futures

[ramjig]

I used NullCalendar still noticing the rates are not close to Fabozzi's numbers. Any suggestions?

 

Thanks
Ramji

 

------------------------------

Faboozi calculated casflows as follows.

 

Futures rate = 100 -Eurodollar Future Price. (In the following table second column represents futures rate).

 

Cash flow = notional amount  * futures rate * ( days in period / 360). The first column represents cash flow per each quarter.

 

period forward rate = annual forward rate * (days in period / 360)

 

forward discount factor of period 1  = 1 /  (1 + (period forward rate of 1 /100) )

 

In general

     forward discount factor of period t = 1  / (  (1 + (period forward rate of 1 /100) ) * (1 + (period forward rate of 2 /100) ) * .... * (1 + (period forward rate of t /100) )  )

 

PV of Cash flow of period t =  Cash flow of period t *  forward discount factor of period t.

 Last column in the followig table was calculated using the above formula.

 

 

Amount: 1012500-----Rate:0.0405----Days: 90 --- 1002351 (PV of Cash Flow)
Amount: 1049028-----Rate:0.0415----Days: 91 --- 1027732
Amount: 1162778-----Rate:0.0455----Days: 92 --- 1126079
Amount: 1206222-----Rate:0.0475----Days: 92 --- 1154229
Amount: 1225000-----Rate:0.0490----Days: 90 --- 1158012
Amount: 1271472-----Rate:0.0503----Days: 91 --- 1186852
Amount: 1316111-----Rate:0.0515----Days: 92 --- 1212562
Amount: 1341667-----Rate:0.0525----Days: 92 --- 1219742
Amount: 1350500-----Rate:0.0540----Days: 90 --- 1210970
Amount: 1390278-----Rate:0.0550----Days: 91 --- 1229999
Amount: 1443889-----Rate:0.0565----Days: 92 --- 1259248
Amount: 1472000-----Rate:0.0576----Days: 92 --- 1265140

 

Thanks

Ramji

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[Luigi Ballabio]

On Sun, 2009-12-20 at 15:58 -0500, [hidden email] wrote:
> I used NullCalendar still noticing the rates are not close to
> Fabozzi's numbers. Any suggestions?

Ok, I finally found some time to have a look.  Your coupon dates are not
aligned with the futures dates.  You're creating the futures on IMM
dates, which means that they go:

from June 15th, 2005 to September 15th, 2005;
from September 21st, 2005 to December 21st, 2005;
from December 21st, 2005 to March 21st, 2006;
from March 15th, 2006 to June 15th, 2006;
from June 21st, 2006 to September 21st, 2006;
from September 20th, 2006 to December 20th, 2006;
from December 20th, 2006 to March 20th, 2007;
from March 21st, 2007 to June 21st, 2007;
from June 20th, 2007 to September 20th, 2007;
from September 19th, 2007 to December 19th, 2007;
from December 19th, 2007 to March 19th, 2008.

To reproduce the rates exactly, the coupon dates should match the above.
Instead, you're creating the leg schedules with January 1st as start
date, which means you'll have coupons from January 1st to April 1st,
from April 1st to July 1st etc.  If you change the schedule (for
instance, if you replace:

Date maturity = settlementDate + lenghtInYears*Years;

with:

Date startDate = Date(21,March,2005);
Date maturity = startDate + lenghtInYears*Years;

and create the schedules from startDate to maturity, some of the coupon
dates will match (not all of them, unfortunately, as the IMM dates are
less regular) and so will some of the rates:

Amount: 1.04932e+06-----Rate: 0.0410605-----Days: 92
Amount: 1.0671e+06-----Rate: 0.0417562-----Days: 92
Amount: 1.15014e+06-----Rate: 0.0455-----Days: 91
Amount: 1.18e+06-----Rate: 0.0472-----Days: 90
Amount: 1.25637e+06-----Rate: 0.0491624-----Days: 92
Amount: 1.28544e+06-----Rate: 0.0503-----Days: 92
Amount: 1.30224e+06-----Rate: 0.051517-----Days: 91
Amount: 1.3129e+06-----Rate: 0.0525162-----Days: 90
Amount: 1.38e+06-----Rate: 0.054-----Days: 92
Amount: 1.40604e+06-----Rate: 0.0550191-----Days: 92
Amount: 1.42899e+06-----Rate: 0.0565317-----Days: 91
Amount: 1.45735e+06-----Rate: 0.0576536-----Days: 91

If you set the start date to March 20th or 19th, you'll match other
rates.

Luigi



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