Presentazione venice modificata

Cheapest to delivery option and credit risk in
European bond future market
Back to the future
Cristiana Corno
Structuring, Rates & Inflation
European Debt Crisis: from Threat to Opportunity?
Venice, September 19-21 2012

Back to the future 1
Summary
The bond future is literally a “standardized forward agreement in which the seller agrees to deliver physically to
the buyer a notional amount of nominal bond at a certain date versus payment of an invoice price”.
The deliverable assets are specified by the bond future contract grade and make up the deliverable basket.
The peculiarity of bond future is that the seller has the choice on “which eligible bond to deliver” and “when to
deliver it”.
These rights make up the short’s STRATEGIC DELIVERY OPTIONS.
The bond future MULTIASSET NATURE makes it one of the most traded hybrid.
SHORT’S DILEMMA

Reasons to go back
I thought it could be interesting to review this topic, because in the recent past we have witnessed both:
an increase of the range of tradable products;
an increase in the optionality priced in bond future markets.
Therefore, in the following, we will:
briefly review basis terminologies and concept with particular reference to the delivery option;
look at what happened recently which has affected bond future optionality;
try to identify challenges and opportunities offered by the product.
For avoidance of doubts, the jump was from
21st October 2015 to 26th october 1985

• Why back to the future? Optionality and new products•• Why back to the future? Optionality and new productsWhy back to the future? Optionality and new products
Agenda
• Opportunities and challenges•• Opportunities and challengesOpportunities and challenges
• Basis basics: terminology and concepts•• Basis basics: terminology and conceptsBasis basics: terminology and concepts

Basis Basics: general
Basis is a concept common to all future/forward market. In the commodities market, the basis is the difference
between the spot and forward price.
BASIS = SPOT PRICE – FORWARD PRICE
In commodities market, being,
FORWARD PRICE = SPOT PRICE + COST OF FUNDING + COST OF STORAGE
the basis tends to equilibrate the cost of funding and storage or
BASIS = -(COST OF FUNDING + COST OF STORAGE)‫‏‬
and it is generally negative, with Forward > Spot.
In bond market, cost of storage in null, plus the asset offers an income stream therefore basis is defined by :
BASIS = -COST OF FUNDING + INCOME STREAM = TOTAL CARRY
and is positive/negative in relation to the yield curve slope.
In a positively inclined yield curve carry is positive as it is the basis with Forward price < Spot price.
By definition BASIS CONVERGE TO ZERO AT CONTRACT EXPIRY

Basis Basics: general
BTPS 5 ½ 09/01/22 BASIS
0
0.2
0.4
0.6
0.8
1
1.2
1.4
10 12 14 18 20 24 27 31 33 35 39 41 45 47 49 53 55 59 61 63 67 69 73 75 77 81 83 87 89 91 95 97
DAYS TO EXPIRY
SPOTPRICE-FORWARDPRICE
Analytically:
BASIS = SPOT - FORWARD
with spot = Ps and forward = [ Ps + ai(t) ] * ( 1 + r(T-t) ) - ai(T), we get:
BASIS = Ps - [( Ps + ai(t) ) + (Ps + ai(t)) * r(T-t) - ai(T)], or
BASIS = - (Ps + ai(t)) * r(T-t) + ai(T) – ai(t)
BASIS = -cost of funding + income coupon = total carry = daily carry * number of days
We expect the basis to be 0 at contract
expiry and to decrease with time
proportionally to the daily carry, with the
main factor of volatility being the repo rate.
)(**)(** tTrMDtTr
y
P
P
Basis s
s
−−=−
Δ
Δ
−=
Δ
Δ
)(*))(( tTtaiP
r
Basis
s −+−=
Δ
Δ

Basis Basics: bond future
Compared to other futures, bond future are more complicated, because the underlying asset is a theoretical
government bond with a fixed specific coupon (6% in europewide) and range of maturity (8.5-11 for Btp future,
8.5-10.5 for bund, 8.5-13 for Gilt).
The contract is settled by physical delivery and permits the delivery, by the short, of any coupon security, provided
it meets the deliverability criteria (usually remaining maturity, amount outstanding, date of issue called “contract
grade” or “contract specifications”). The eligible securities are said to be in the deliverable basket.
In the European bond futures markets the delivery period is just one day therefore the timing option, related to
“when to deliver” are irrelevant for the European market.
In the Us, due to the different delivery process, other than the “quality” option, the set of options includes:
the “month end option” (future’s last trade date is seven business days before last delivery date);
the “timing” option, divided in “carry option” (one entire month for delivery) and the “wild card” option (time
window between future settlement price establishment and end of notification time for short investor
willing to deliver).

European less hybrid than Us peers
YYYWild card Option
YYNCarry option
YNNEnd of the month option
YYYQuality option
CBTLIFFEEUREX
In terms of their relative importance the switch option is, by far, the most valuable followed by the “month end option”,
while the timing options have shown small importance at all. (Burghardt, “The treasury bond basis”).
Literature shows that the value of the shorts option is highest when rates nears notional coupon level or the inflection
point, where there is high probability of switch between high and low duration bonds.
Below we summarize the set of options that the short of futures owns in the different markets.
Increase
in
quantity
Increase
in
value

Basis Basics: bond future
The multi asset nature of the future had the objective to make demand for bonds for the purpose of
delivery less concentrated in order to avoid overpricing and squeeze.
To make the deliverable security economically equal to deliver the CBOT decided to adopt, when introducing the
T-bond future (1977), the conversion factor invoicing system.
The aim of the conversion factor system was to adjust the invoice price paid by the long upon delivery to the
characteristics of the bond being delivered, make them economically equivalent into delivery and close to their
market prices.
Upon delivery of bond (i) the long future pays the short an invoice amount equal to:
INVOICE PRICE = CF(i) * FUTURE + ACCRUED INTEREST(i)‫‏‬

Basis Basics: conversion factor
The conversion factor is a fixed amount defined by the exchange for each bond and each future expiry and
it is approximately equal to the forward price of each bond at delivery for which the yield to maturity is equal
to 6% or the notional coupon ( in next slide easy calculation on bbg).
For construction the CF depends only by the cash flow structure of each bond at delivery. It does not depend on
market conditions. Its aim is to compensate the long into delivery for the different bond structure in term of coupon
and maturity, with respect to the notional underlying bond.
It partially does its job: for example bond with coupon higher than 6% will be higher than 1 and, vice versa, this
effect will be greater depending on the bond maturity.
As we will see all the CTD problem can be referred to a conversion factor fault.

Basis Basics: approximate conversion factor
With Bloomberg function Yas it is
possible to calculate the bond forward
price at delivery with 6% yield to
maturity: price equals conversion factor

Basis Basics: bond future pricing
Ideally, at delivery, to make the short indifferent between delivering any of the eligible bonds, the future invoice
price CF(i)*F+ AI(i) of each bond should equal its purchase price in the market or S(i)+AI(i).
Unfortunately in the current system, bonds will be equivalent at delivery:
CF (i)* F = S(i) for each i
only at flat 6% yield curve, where CF(i)=S(i) for each i, with future = 100.
Each time we move away from this ideal condition, the CFS it is not able to equalize differences in bonds % and
we will have one or more cheapest to deliver (CTDs) bonds.
In all these cases at delivery, for non arbitrage argument*, we will have:
S(i) >= CF(i)* F
for each i.
* Non arbitrage argument1: If S(i) < CF*F then the short can buy i and deliver it into the future by making profit: CF*F-S(i) > 0, reverse can not be done

⎥
⎦
⎤
⎢
⎣
⎡
=
)(
)(
min/
iCF
iS
ictd i
Given that at delivery S(i) >= CF*F for each bond i, the short ‘s profit will be <=0 and he will try to
maximize his PROFIT function:
PROFIT% = (INVOICE PRICE – PURCHASE PRICE)/(PURCHASE PRICE)
by delivering the bond i with the lowest converted price S(i)/CF(i):
At delivery CTD is the bond is defined as the bond i:
And the future price at delivery will equal to:
)(
)(
ctdCF
ctdS
Fdelivery =
( )
( )
1
***
,
,,
−=
−
=
+
+−+
=Π
i
i
i
ii
delii
deliidelii
S
CFF
S
SCFF
AIS
AISAICFF

⎥
⎦
⎤
⎢
⎣
⎡
≤
)(
)(
CtdCF
CtdFwd
F t
t
During the life of the contract, the future price will be:
Future price will be lower than the forward converted price of the cheapest to deliver to compensate
the fact that the CTD bond could change. The CTD will be the bond which maximize the short seller
profit.
The difference between current future price and lower forward converted price is the value of the delivery
options in the hands of the short investor.
t
t
F
ctdCF
ctdFwd
−==
)(
)(
(DOV)ueoption valdelivery α

Basis Basics: delivery option in chart
Here, we rappresent, graphically, the delivery option. Its value, at time t, is the difference between the future
price and lower converted price of the bonds in the deliverable basket.
The value of the delivery option is a function of the probability of switch (greater near switch point) and also of
the relative payoff in case of switch (omogeniety of the basket, graphically rappresented by the slope of the
price/yield relationship).
Illustration inspired by Burghardt: for each
bond we graph the forward converted price.
The difference between forward converted
and future price, a t time t, is the value of the
delivery option (yellow) .

Basis Basics: gross basis
FiCFiSiBasis *)()()( −=
The gross basis in bond future is defined as:
and it represents the difference between the spot price and the future implied forward price for bond i.
The basis can be decomposed (by adding and subtracting the forward price Fwd(i)) into:
At delivery, basis will converge to the net basis.
and it will be zero for the CTD bond and equal to the difference between the spot price and the converted price
for each other bond, as to say a measure of the expensiveness to deliver it.
FiCFiFwdiFwdiSiBasis *)()()()()( −+−=
)()()( iNetbasisiCarryiBasis +=
settlementidelivery FCFiSiBasis *)()( −=

Basis Basics: net basis
Net basis or basis net of carry BNOC is defined as:
BNOC(i) = BASIS(i) - CARRY(i) or, as seen before:
Since, as we have see, the delivery option value has been defined as:
the BNOC is an approximation of the delivery option value. It is a pure option value only for the cheapest
to deliver bond, for which holds:
For the other deliverable it is a mix of delivery option value and distance of the bond forward price from the CTD
forward (a measure of expensiveness)
t
t
F
ctdCF
ctdFwd
−==
)(
)(
(DOV)ueoption valdelivery α
)(*)(*)()(n ctdCFctdCFFctdFwdBNOCetbasis tt α=−=
[ ])()(*)()()( iFwdiSFiCFiSiBNOC −−−=
FCFiFwdiBNOC i *)()( −=

Basis Basics: gross and net basis in numbers
Spot Price Yield Fwd Price Fwd Yld CF Fwd/CF Gross Basis Carry=S‐Fwd Net Basis Net basis at delivery
CTD Basket #NAME? #VALUE! NA NA
BTPS 5 1/2 09/01/22 103.4 5.1249 102.101 5.29 96.96880 105.29259 1.68 1.30 0.380687 0.329143
BTPS 4 3/4 08/01/23 97.1 5.1646 96.000 5.31 90.90224 105.60789 1.74 1.10 0.643486 0.595166
BTPS 5 03/01/22 100.3 5.0208 99.121 5.18 93.57107 105.93164 2.14 1.18 0.965312 0.915574
BTPS 4 3/4 09/01/21 99.36 4.8968 98.242 5.06 92.15330 106.60693 2.69 1.12 1.572989 1.524004
BTPS 3 3/4 08/01/21 92.44 4.8612 91.577 5.02 85.55955 107.03342 2.69 0.86 1.825343 1.779863
BTPS 5 1/2 11/01/22 102.96 5.1859 101.673 5.35 96.87481 104.95316 1.34 1.29 0.051494 0.000000
The NET BASIS is a pure option value only for the CTD bond only, for all other bonds it is a mix of
delivery option and amount by which the issue is expensive to deliver.
BTP SEP22 NET BASIS IN UKZ2 (CTD)
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
6/4/2012
6/11/2012
6/18/2012
6/25/2012
7/2/2012
7/9/2012
7/16/2012
7/23/2012
7/30/2012
8/6/2012
8/13/2012
8/20/2012
8/27/2012
Net basis at delivery = 0 for ctd bond
and equal to = S – cf *F for others. Can
be thought as the cost of the option to
exchange the vond for the CTD.
(payout of a call on S with strike CF*F)

Basis Basics: net basis and IRR
As we have seen, during the life of the contract, the CTD bond will maximize the short profit:
Therefore CTD bond will minimize the % net basis.
If we define the implied repo rate (IRR) as the rate of return of a cash & carry strategy with delivery of the
bond into the future, then the CTD is the bond which minimizes the difference between the implied repo
rate (IRR) and the actual repo rate:
It is possible to show that:
The IRR rate will be lower than the corresponding actual repo rate to take in account possible change in
CTD bond, in the same way as the future price is lower than the converted forward.
ggicePurchase
icePurchaseiceInvoice
IRR
360
*
Pr
PrPr
⎟
⎠
⎞
⎜
⎝
⎛ −
=
⎥
⎦
⎤
⎢
⎣
⎡
+
−
=
AiP
ctdCFFctdFwd
Min
s
tt )(*)(
IRR)-o(ActualRepMin
To identify the CTD we use the IRR method, which is a sort of %net basis.
( )
( ) tiitii
ii
tii
deliidelii
AIS
netbasis
AIS
FwdCFF
AIS
AIFwdAICFF
,,,
,, **
+
=
+
−
=
+
+−+
=Π

Basis Basics: conversion factor bias and ctd problem
If the conversion factor invoicing system was working properly, all the bonds in the basket would be equally
economic to deliver (S(i) = CF(i)*F and future price would equal 100).
Unfortunately this is true only when:
the yield of curve is flat
and equal to the notional coupon (6%)
Any time we are away from this ideal situation, we will have one or more cheapest to deliver securities.
All the cheapest to deliver optionality derives from a fault* in the invoicing system and the CTD phenomenon can
be traced mainly to a bias associated with the mathematics of the conversion factor.
*To overcome the misfunctionality of the conversion factor system in 2006 (Oviedo, “Improving the design of Treasury-Bond future contract”) a
new system has been proposed in literature TRUE NOTIONAL BOND SYSTEM, which would makes all the deliverable bonds equal for any level
of flat curve, while in the CFS this is achieved only at a specific level of yield equal to the notional coupon.

Basis Basics: conversion factor bias and CTD problem
⎥
⎦
⎤
⎢
⎣
⎡ −+−−
==
%)6(
*%)6(*5.0*%)6(%)6(
%)6(
)()( 2
i
iii
i
i
i
i
S
CVXTYyMDyS
S
yS
CF
yS
The CTD bond at expiry will minimize the ratio S(i)/CF(i).
Since CF(i) is approximately the price at delivery of bond i on a flat yield curve at 6%, we can rewrite
the ratio:
Therefore which bond will be deliverable, depends on their relative sensitivities to yield
change as expressed by modified duration and convexity.
In general, when yield are below 6% the cheapest to deliver will be the lowest duration bond and
vice versa when yields are above 6% the cheapest to delver bond will be the higher duration bond.
For similar duration bond the cheapest to deliver bond will be the less convex bond.
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −+−−
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
%)6(
*%)6(*5.0*%)6(
min
)(
min
2
i
ii
i
i
S
CVXTYyMDy
CF
yS

Below, a graphical representation of the conversion bias and CTD change with 2 bonds of different and
equal duration.
Before delivery the future will track the bond with lower converted forward price: the long will receive
always the worst performing bond in the deliverable basket. This gives it a NEGATIVE CONVEXITY
feature compared to the deliverable bonds. The price of the convexity is the delivery option value.

Converted prices for deliverable IKZ2
89
91
93
95
97
99
101
103
105
107
109
4.58
4.68
4.78
4.88
4.98
5.08
5.18
5.28
5.38
5.48
5.58
5.68
5.78
5.88
5.98
6.08
6.18
6.28
6.38
6.48
6.58
yield level
FWD(i)/Cf(i)
8/1/2023
9/1/2022
11/1/2022
In chart below, we chart the forward converted price for Btp deliverables in Dec12 contract for simulated forward yield
with the corresponding net basis at delivery to identify the possible CTD switch.
Considering only parallel shift there is one switch point around 6.10% in yield (ref Aug21)
Net basis at delivery for IKZ2
0
0.5
1
1.5
2
2.5
3.04
3.24
3.44
3.64
3.84
4.04
4.24
4.44
4.64
4.84
5.04
5.24
5.44
5.64
5.84
6.04
6.24
6.44
6.64
6.84
8/1/2023
9/1/2022
11/1/2022
6% switch point

Basis Basics: option delivery value
The value of the delivery option depends on the probability and by the outcomes of a CTD change (nearness to switch
point and difference in slope of the 2 curves). Therefore the option value depends on:
yield change
slope change
unanticipated new issues.
Yield change. As seen, the CTD bond is related to the level of yields. It will tend to be the lowest duration bond
for yield lower than 6% and vice versa. It will generally, be the least convex bond. The value of the delivery option
will depend on the yield volatility and on bonds different sensitivities to yield changes (homogeneity of the
basket).
Yield slope. We can distinguish 2 kind of slope move with opposite effect the delivery option.
“Systemic move”: generally, as yield rise curve flattens and vice versa. This kind of move has the effect to
reduce the option value by reducing the switch probability. We can appreciate how this happens from chart
in next slide.

Systemic move: as yield come down on higher duration bond, curve steepens and lower duration bond outperform,
shifting its curve from LD to LD’. The switch point fades away decreasing the slope of the basis.
Systemic slope move
reduce option value by
moving away switch
points. Due to
correlation between
slope and level a
systemic move will
decrease the net basis
change for same
difference in yield
Switch point 1
Switch point 2
Initial Future
Final Future

Switch points move when considering slope too...
0
0.2
0.4
0.6
0.8
1
1.2
4.042324.142324.242324.442324.542324.642324.742324.842324.942325.042325.142325.242325.342325.442325.542325.642325.742325.842325.942326.042326.142326.242326.342326.442326.542326.642326.742326.842326.94232
8/1/2023 shift only
11/1/2022 shift only
8/1/2023 slope
11/1/2022 slope
As an example, in chart below, we plot net basis for Btp Dec12, at delivery in 2 hypothesis :
1. parallel shift only;
2. parallel shift and slope move using historical beta (using Aug21 as benchmark we simulate yield for the
benchmark and calculate joint distribution using historical betas)
S1 S2
Also the switch point
depend on the beta, the
higher the beta (to the
shortest bond being
moved) the further out
goes the switch point
beta Sep22 versus Aug21 switch_point
0.85 5.52%
0.875 5.60%
0.9 5.94%
0.925 6.34%
0.95 6.83%

Unsystemic move: at constant yield a steepening of the curve (LD from LD’ higher performance of low duration
bond) shift the switch point from S to S1 decreasing the basis. Vice versa a flattening of the curve (shift of the initial
curve from LD to LD’’) shifts the switch point from S to S2 increasing the basis.
At constant yield on the
high duration bond, the
steepening reduces the
basis and the flattening
increases it.
Pure slope movement
will increase the
volatitlity of switch
points and the value of
the delivery option

The announcement of issuance of new bonds, which will become cheapest to deliver represents a source of risk for
basis trading. This is likely to happen, when rates are trading near the coupon rate.
As an example, below, what happened at the basis of Mar20 in the June2011 contract when the issuance of Sep21
was announced (18° February 2011).
CTD net basis in IKH2 on new issuance
0
0.1
0.2
0.3
0.4
0.5
0.6
1/3/2011
1/5/2011
1/7/2011
1/9/2011
1/11/2011
1/13/2011
1/15/2011
1/17/2011
1/19/2011
1/21/2011
1/23/2011
1/25/2011
1/27/2011
1/29/2011
1/31/2011
2/2/2011
2/4/2011
2/6/2011
2/8/2011
2/10/2011
2/12/2011
2/14/2011
2/16/2011
2/18/2011
2/20/2011
2/22/2011
2/24/2011
2/26/2011
2/28/2011
3/2/2011
3/4/2011
3/6/2011
3/8/2011
Announcement

• Why back to the future? New products and optionality back•• Why back to the future? New products and optionality backWhy back to the future? New products and optionality back
Agenda

New products
From the beginning of the European crisis, to encounter hedging/downloading needs the available bond futures have
increased notably with:
Eurex adding three new bond future on the Italian curve: short (Oct 2010), medium (Sep 2011) and long
end (Sep 2009) and a long end bond future on the Oat market (Apr 2012);
Meff adding a long end bond future on the Spanish government market (May 2012). Unfortunately not
very successfully.
Here, below, you can find the main features of the contract specification for the Btp futures.
Two exchange days prior to the delivery day of the relevant maturity month. End of trading for the maturing delivery
month is 12:30 CET
Last trading day
The tenth calendar day of the respective quarterly month, if this day is an exchange day; otherwise, the exchange
day immediately succeeding that day.
Delivery day
A delivery obligation arising out of a short position may only be fulfilled by the delivery of certain debt securities
issued by the Republic of Italy with a remaining term of respectively 2 to 3.25 years (short-term), 4.5 to 6 years
(mid-term) and 8.5 to 11 years (long-term) and an original maturity of no longer than 16 years. Such debt securities
must have a minimum issue amount of EUR 5 billion and a nominal fixed payment.
Starting with the contract month of June 2012, debt securities of the Republic of Italy have to possess a minimum
issuance volume of EUR 5 billion no later than 10 exchange days prior to the last trading day of the current front
month, otherwise, they shall not be deliverable until the delivery day of the current front month contract.
Settlement
Notional short-, mid- and long-term debt instruments issued by the Republic of Italy with a remaining term of 2 to
3.25 years (short-term), respectively 4.5 to 6 years (mid-term) and 8.5 to 11 years (long-term) with a notional
coupon of 6 percent. Mid- and long-term debt instruments must have an original maturity of no longer than 16
years.
Undelyings
Delivery
basket freeze
(Jan2012)

Optionality is back
Optionality in the European bond future market is related only to the possible changes in the CTD. This option
becomes more valuable when:
I. yield and yield slope volatility increases;
II. level of rates nears the notional coupon of the theoretical bond underlying;
III. forward volatility increases.
All of these factors are and have been in place lately.
I. Credit risk has increased yield volatility, while institutional intervention (ltro, non standard intervention talking) has
increased slope volatility by interfering with the curve shape (a comparison of net basis for Btp and Bund future in
chart1).
II. Btp rates have often reached the 6% nominal coupon of the bond future, while Liffe in October 2011 has lowered
the notional coupon from 6% to 4% (Gilt net basis behaviour in chart 2).
III. Forward price is a function of both spot price and repo rate. With the repo rate stuck the volatility of the forward
rate has increased.

Optionality is back: credit risk and institutional intervention
Net basis in 10y Btp and Bund from 2009 onwards
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
29-Sep-09
29-Oct-09
29-Nov-09
29-Dec-09
29-Jan-10
28-Feb-10
29-Mar-10
29-Apr-10
29-May-10
29-Jun-10
29-Jul-10
29-Aug-10
29-Sep-10
29-Oct-10
29-Nov-10
29-Dec-10
29-Jan-11
28-Feb-11
29-Mar-11
29-Apr-11
29-May-11
29-Jun-11
29-Jul-11
29-Aug-11
29-Sep-11
29-Oct-11
29-Nov-11
29-Dec-11
29-Jan-12
29-Feb-12
29-Mar-12
29-Apr-12
29-May-12
29-Jun-12
29-Jul-12
29-Aug-12
ctd_btp_net_basis
ctd_bund_net_basis
Net basis in Btp future has become more valuable due to:
I. higher credit risk: increase in yield volatility and in the level of rates, reaching the 6% notional coupon of the bond
future or the “inflection point”;
II. institutional intervention has affected market in two ways: increasing yield slope volatility and lowering the
correlation between repo and long rates thereby augmenting the forward volatility

Forward prices are a function of spot price and repo rate:
Pf = [ Ps + ai(t) ] * ( 1 + r(T-t) ) - ai(T)
An increase in rates has the effect:
To lower the forward price via a reduction in spot price
To increase the forward price via an increase of the funding cost
Optionality is back: credit risk and institutional intervention
Even if in the short term the two
rates respond to different forces,
they showed a positive correlation
in the past R^=0.43%.
With repo stuck, independent by
market forces correlation has gone
down, and forward volatility has
increased*.
222
),()()(),()()(2)()()()()( yxCovyVxVyxCovyExExEyVyExVxyVar ++++=Application to Pf formula of the following
With Cov(X,Y) going from negative to zero

Optionality is back: nearing inflection point
Net basis in 10y Gilt from Sep 2009 onwards
-1
-0.5
0
0.5
1
1.5
2
31-Aug-12
26-Jul-12
21-Jun-12
16-May-12
11-Apr-12
5-Mar-12
26-Jan-12
21-Dec-11
15-Nov-11
11-Oct-11
6-Sep-11
1-Aug-11
27-Jun-11
20-May-11
13-Apr-11
9-Mar-11
1-Feb-11
28-Dec-10
22-Nov-10
18-Oct-10
13-Sep-10
6-Aug-10
2-Jul-10
28-May-10
22-Apr-10
15-Mar-10
5-Feb-10
31-Dec-10
25-Nov-09
20-Oct-09
gilt_net_basis
Same ctd for 6 consecutive rolls
In October 2011 Liffe has lowered the Gilt notional coupon from 6% to 4%:
I. to reckon a lower long term level of interest rates;
II. to give back duration to the future. The wide distance between notional coupon and the actual level of rates have
made the shortest bond CTD for six consecutive rolls with a effective shortening of the future duration.

• Why back to the future? Optionality and new products•• Why back to the future? Optionality and new productsWhy back to the future? Optionality and new products
Agenda

Opportunities & challenges: how to value delivery option
The first challenge is to be able to price the delivery option. At this aim 4 steps are necessary.
Have a precise idea of deliverable bonds forward distribution and of the way to model it (1-2 factor model).
Calculate for each state of the world the ctd and the implied future price.
Calculate the value of the net basis for each deliverable in each state of the world.
Average the each state of the world net basis by its risk neutral probability.
This is important both:
for pricing (evaluate future richness/cheapness versus theoretical)
and for hedging. If we do not consider the delivery option each time the CTD changes we have a jump in
future DV01 (pictures below).

Opportunities & challenges: trading strategies
We briefly review the trading opportunities in basis trading.
Sell the CTD net basis equivalent to sell the delivery option: like all the short options trade it has limited
profit and unlimited loss potential. It is a carry trade: if nothing happens net basis goes to zero. Trade is
based on:
Valuation of implicit optionality (theoretical versus actual, optionality judged too high, future too rich)
Seasonal patterns
Outcome of negative scenario
Net basis in 10y Btp contract
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
29-Sep-12
01-Oct-12
03-Oct-12
05-Oct-12
07-Oct-12
09-Oct-12
11-Oct-12
13-Oct-12
15-Oct-12
17-Oct-12
19-Oct-12
21-Oct-12
23-Oct-12
25-Oct-12
27-Oct-12
29-Oct-12
31-Oct-12
02-Nov-12
04-Nov-12
06-Nov-12
08-Nov-12
10-Nov-12
12-Nov-12
14-Nov-12
16-Nov-12
18-Nov-12
20-Nov-12
22-Nov-12
24-Nov-12
26-Nov-12
28-Nov-12
30-Nov-12
02-Dec-12
04-Dec-12
06-Dec-12
08-Dec-12
ikz9 ikh10
ikm10 iku10
ikz10 ikh11
ikm11 iku11
ikz11 ikh2
ikm2
Seasonality of Btp net basis

Sell/buy the basis on non-CTD bond. Strategy uses relative cheapness/richness of future to express relative views
versus other bonds (auction play, relative value) or directional play leveraged by future convexity. Due to future
convexity basis trading show option like behaviour. Specifically:
a long basis position on a high duration bond will look like a call on bond and will benefit from
flattening
Long high duration
basis is like a bond
call with cost equal to
the net basis.
It will also benefit from
flattening

A long basis position on a low duration bond will look like a put on bond and will benefit from
steepening
Long low duration
put.
It will also benefit
from steepening.

A long basis position on a mid duration bond will look like a straddle and actually perform with the fly.
Long mid duration
straddle.
It will also perform
with the fly.

Converted price for deliverable IKZ2
85
90
95
100
105
110
115
120
125
130
135
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.25
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
7.00
7.25
Yield Level
Fwd(i)/CF(i)
8/1/2021
8/1/2023
9/1/2021
3/1/2022
9/1/2022
11/1/2022
As an example we plot converted price and net basis for BTP dec12 for different yield levels. Using a simple parallel
shift move we get a unique switch near 6%
Net basis for deliverables in IKZ2
0
0.5
1
1.5
2
2.5
3
3.45
3.65
3.85
4.05
4.25
4.45
4.65
4.85
5.05
5.25
5.45
5.65
5.85
6.05
6.25
6.45
6.65
6.85
7.05
7.25
Yield Level
Netbasis
8/1/2021
8/1/2023
9/1/2021
3/1/2022
9/1/2022
11/1/2022
If we introduce a systemic slope move (correlated with level via beta), we get different results based on the
assumption we make for Btp Nov22 beta (see table).
5.550.90.9
5.750.90.92
00.90.95
00.90.98
switch_pointbtp aug23btp nov22
Using the same beta for Btp Nov22 as Btp
Sep22 (beta=0.98) we get 0 switch point.

Apparently the probability of switch is low, but if we look more in detail the switch jump is a function of the slope
between Nov22 and Aug23. By twisting only that segment we get that the switch in ctd at constant repo will happen
with the spread at 7.
Net basis with curve twist
0
0.5
1
1.5
2
2.5
-0.22
-0.20
-0.18
-0.16
-0.14
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
8/1/2023
11/1/2022
Switch level in term of spread Nov22-Aug23
Where we are now... Some value in being long the option

Opportunities & challenges: possible other uses.
Use bond future to get prices for new issues expected to be in the deliverable basket (as was the case for
Btp Nov22)
Volatility arbitrage. Given delivery option valuation framework it is possible to gather information from future
market on volatility and compare it with bond option market.
WE WILL DO OUR BEST TO PROVIDE YOU WITH ANALYSIS AND OPPORTUNITIES IN
THE NEXT.................. FUTURE

Bibliography
“The treasury bond basis”, 3° edition, Burghardt.
“The future bond basis”, 2° edition, Choudhry
““Basis evaluation in bond future markets”, Corielli & Rindi 1995
Understanding US treasury futures”, CME publication
“European bond futures guide”, JpMorgan, F. Bassi 2006
“Improving the design of treasury bond future contracts”, Oviedo 2003
“Valuing bond futures and the quality option”, Carr & Chen 1997

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