The following example demonstrates analyzing German Euro-Bund futures traded on Eurex.
bndfutimprepo apply to bond futures in the U.S., U.K., Germany,
and Japan. The workflow for this analysis is:
Calculate bond conversion factors.
Calculate implied repo rates to find the CTD bond.
Price the bond future using the term implied repo rate.
Use conversion factors to normalize the price of a particular bond for delivery in
a futures contract. When using conversion factors, the assumption is that a bond for
delivery has a 6% coupon. Use
convfactor to calculate
conversion factors for all bond futures from the U.S., Germany, Japan, and
For example, conversion factors for Euro-Bund futures on Eurex are listed at
www.eurexchange.com. The delivery date for Euro-Bund
futures is the 10th day of the month, as opposed to bond futures in the U.S., where
the short position has the option of choosing when to deliver the bond.
For the 4% bond, compute the conversion factor with:
CF1 = convfactor('10-Sep-2009','04-Jul-2018', .04,.06,3)
CF1 = 0.8659
This syntax for
convfactor works fine for bonds with standard
coupon periods. However, some deliverable bonds have long or short first coupon
periods. Compute the conversion factors for such bonds using the optional input
Specify all optional input arguments for
CF2 = convfactor('10-Sep-2009','04-Jan-2019', .0375,'Convention',3,'startdate',... datenum('14-Nov-2008'))
CF2 = 0.8426
To determine the availability of the cheapest bond for deliverable bonds against a
futures contract, compute the implied repo rate for each bond. The bond with the
highest repo rate is the cheapest because it has the lowest initial value, thus
yielding a higher return, provided you deliver it with the stated futures price. Use
bndfutimprepo to calculate repo
% Bond Properties CouponRate = [.0425;.0375;.035]; Maturity = [datenum('04-Jul-2018');datenum('04-Jan-2019');datenum('04-Jul-2019')]; CF = [0.882668;0.842556;0.818193]; Price = [105.00;100.89;98.69]; % Futures Properties FutSettle = '09-Jun-2009'; FutPrice = 118.54; Delivery = '10-Sep-2009'; % Note that the default for BNDFUTIMPREPO is for the bonds to be % semi-annual with a day count basis of 0. Since these are German % bonds, we need to have a Basis of 8 and a Period of 1 ImpRepo = bndfutimprepo(Price, FutPrice, FutSettle, Delivery, CF, ... CouponRate, Maturity,'Basis',8,'Period',1)
ImpRepo = 0.0261 -0.0022 -0.0315
bndfutprice to perform price
calculations for all bond futures from the U.S., Germany, Japan, and U.K. To price
the bond, given a term repo rate:
% Assume a term repo rate of .0091; RepoRate = .0091; [FutPrice,AccrInt] = bndfutprice(RepoRate, Price(1), FutSettle,... Delivery, CF(1), CouponRate(1), Maturity(1),... 'Basis',8,'Period',1)
FutPrice = 118.0126 AccrInt = 0.7918