Section 4 The purpos
4: Mark-t se of this se
9 Professor
4: Mark-t se of this se is package h
ues are calc value assoc e bond minu effects on th ove in isola different fac
noting that largely offs alue while a ng in sign th ple, when an d value and
market-to-m pective this e zero. As
:
r Shyan Yuan
to-Market ection is to a has been en culated by p
iated with t us the price he CDS leg ation, the ba ctors individ
because ba etting; i.e. a at the same t hey may not n issuers cre cash flows
market valu s means at in
s the CDS c
n Lee, “Cred
t Change analyze the ntered, as op product, and the changing e at which th
of the basis asis is explo
dually is im
asis trade is an increased
time bond v t be in magn edit rating is
on the basi
ue of a CDS nception va curve chang
it Derivatives 23
s in the V mark-to-ma pposed to be d not explici g market pr he bond was
s package. F oiting disloc mportant.
a fully hedg d default ris values are fa
nitude. Also s downgrad is trade, whi
S on inceptio alue of the d ges the mark
s and Structu
Value of a arket risks a efore enterin itly ‘netted’
rice of a bon s purchased Finally, whi cations betw
ged position sk portrayed
alling. Ho o, some cha ed, it trigge ile leaving t
on is always default leg m k-to-market
ured Finance
Basis Pac associated w ng the basis
’ by trading nd is simplis d. Thus, I on
ile it is unli ween market
n, Mark-to-m d in CDS ma owever, whi
anges are un ers step-up c the CDS leg
s zero. Fro minus the va
value of the
e” class note
ckage with changin s package. m activit. T stic, the cur nly analyze kely these f ts, thus unde
market chan arket, increa ile some cha nique to one covenants o g unaffected
om the prot alue of the p
e CDS is co
s, Fall Seme
ng factors to-The
mark-rrent traded the mark-factors will
erstand the
nges
tection premium ommonly
ester 2008.
Ann pt Dt
I expand th
Where: The first te market rate the expecte which one the contrac
Mark to m
Changes in First, they spread mat of the carry default we
nuity($) = v = surv = disco his formula
re = change erm is simpl
e CDS curv ed payoffs o
counterpart ct value for
market sens
n the CDS le affect the n tching the m y on the bas
change the
value of CD vival probab ount rate at
to calculate
e in carry current mark
ount rate at vival probab val probabi market CD ginning reco ent recovery ly the prese ve. The dif
on default.
ty would pa both parties
sitivity to p
eg of the tra net carry com maturity on
sis package e present val
S premium bility of defa
year t ed based on
ket CDS spr year t bility of defa
ility of defau DS curve
overy rate a y rate assum ent value of
fference bet This chan ay to “tear”
s is zero.
parallel shif
ade affect th ming from t
the bond (th changes.
lue of payof
24
cash paym ault implied
n the change
read - begin ault implied ult in year t assumption mption
the change tween next t nge in mark-up the cont
fts in CDS
he mark-to-the basis pa he 10yr spre
Second, by ffs received
ents and de d by CDS cu
e in fair valu
nning CDS s d by beginni t implied by
in expected two terms i -to-market v tract by brin
curve:
market valu ackage. By ead in this c y changing t d on default.
fault payme urve
ue of the CD
spread ing CDS cu y the current
d cash flows s the chang value is, in e ng it up to m
ue of basis p y raising or case) we cha the expected . While th
ents
DS as:
urve
t
s, implied b e in present effect, the f market value
package in t lowing the ange the pre d timing of he value rec
by the new t value of fair price
e, where
two ways.
CDS esent value
bond eived
never chan years disco
Figure 14: M
As the cred is gained(l contract pr out. Gain because up premium.
Despite the curve, it is asymmetri deterioratio slow and d
nges, par × ( ounted, and
Mark-to-mark
dit curve sh ost). The ga remium and ns from upw pward shifts
e nearly line important t c. This m on in the cre downward v
(1-R), chang thus the ma
ket sensitivity
hifts up(dow ain recorded d the current ward shifts i s increase th
ear relations to remembe means that su edit quality volatility sm
ging the exp ark to mark
y to parallel s
wn), toward d is equal to t market pre in the credit he probabili
ship betwee er that credi udden upwa of the refer mall.
25
pected time et value.
shifts in CDS
the right(lef o the presen
emium, plus t curve are s ty of defaul
en mark-to-m t risk is a on ard shifts of
rence entity
of receivin
S curve
ft) side of th nt value of th s the increas smaller than lt, lowering
market valu ne-sided jum f the credit c y. Whereas d
ng par chang
he horizonta he differenc
sed probabi n losses for the expecte
ues and para mp risk, thu curve are lik downward s
ges the num
al axis, cont ce between t ility of a def downward ed value of
allel shifts in us volatility kely, given a
shifts are ge mber of
tract value the original fault
pay-shifts the credit
n the CDS is
a enerally
l
Mark-to-m
Like parall CDS contr outs. Unl changes. N the same ti The loss on payments.
Figure 15: M
Mark to m Making ma recovery ra implied de
market sen
lel shifts, ch ract, it chang
like parallel Negative cha ime the redu n the reduct
Positive c
Mark-to-mark
market sens ark-to-mark ate is not a q
fault probab
sitivity to c
hanging the ges the pres l shifts, the anges in slo uced premiu tion in prem changes hav
ket sensitivity
sitivity to c ket changes
quoted rate.
bility, and t
changes in t
slope of the sent value o
effects are ope increase ums and inc miums and c ve equal and
y to changes
hanges in t in value ba . As I show thus has an e
26
the Slope o
e credit curv of the credit
offsetting b e the chance creased cum cumulative s d opposite e
s in the steep
the recover ased on chan
ed before re effect on th
of the CDS
ve has the t premium an based on the e of early de mulative surv
survival dom effects.
pness of the
ry rate:
nging recov ecovery rate
e fair value
curve:
wo effects o nd the prob e structure o efault payme
vival rates r minates the
CDS curve:
very rates is es have a sig
of the CDS
on the fair v bability of de of our steepn ents, a gain reduce cont gain on def
tricky beca gnificant ef S contract.
value of a efault pay-ness
, while at tract value.
fault
ause the ffect on the
The recove volatility is entity issue Recovery r lower reco recovery ra single nam
Figure 16: M
Mark-to-m basis packa may fall si the scenari prepared fo outs becom
ery rate on a s relatively es more deb rates are als very rates, w ates, in gene me CDS is la
Mark-to-mark
market chang age. How gnificantly io in which or significan me more like
a bond is les symmetrica bt (reducing so related to while perio eral, are ver arge.
ket sensitivity
ges in value ever, these as credit ris a basis hold nt mark-to-m ely.
ss volatile t al. Larger g recovery ra o the default
ds with low ry idiosyncr
y to changes
e tend to mo changes are sk increases der receives market vola
27
than the cred changes in ates) or reti t cycle. Peri w default rat ratic and the
s in the recov
ove in the op e not necess s; however, s the largest atility, and e
dit premium n recovery ra res debt (in iods with hi tes have hig e variance o
very rate
pposite dire sarily bad fo
this means t pay-out.
expect volat
m, however ate are likel ncreasing rec
igh default r gh recovery
on realized r
ection expec or the basis companies Thus basis tility to incr
unlike CDS ly when a re covery rates rates tend to rates. How recovery rat
cted returns investor. B
are closer t holder mus rease as def
S premiums eference
s).
o have wever, tes for
on the ond prices to default, st be fault
pay-s
Section 5
One possib contract to entering in in which th intervening effective d exchanged mathemati
The CDS n (value to a slightly to
Where:
5: Basis p
ble modifica buy protec nto a forwar he CDS con g period. T date is later t d until after t cally below
no-arbitrage protection get the no a
n = the co k = the co pt = the cum Φt = cumul
= [the su from 0
=(probab = [pt – p
ackage us
ation to the ction in the f d CDS cont ntract is effe The forward than a vanil
the effectiv w:
e condition sell must eq arbitrage co
ontract matu ontract effec mulative de
ative probab um margina
to k] divide bility of def pk)] / (1 - pk)
sing forw
basis packa future at a p tract today, ective, but a d CDS cont lla CDS wh ve date, even
above, state qual the val ondition for
urity date ctive date efault probab
bility of def al default pr
ed by proba fault from k )] (by Baye
28
ward CDS
age is using pre-specified
the CDS tra assumes the
tract is also ile having t n if the refer
es that the p lue to a prot a k to n yea
bility fault condit robabilities ability of sur k to t) / cum
s’ theorem)
forward CD d premium ader locks i risk of CD of a shorter the same ma rence entity
premium leg tection buye ar forward C
tional on sur from k to t a rvival from mulative surv
)
DS. A For for set leng in a lower p S spread ch r duration, a aturity date.
y defaults. I
g must equa er). I mod CDS:
rvival until and the prob 0 to k vival probab
rward CDS gth of time.
premium for hanges in the
as the contra . No prem
show this r
al the defaul dify this con
t=k
bability of s bility at k
is a By r the period
e act’s miums are
relationship
lt leg ndition
survival
The net eff premium.
credit prem pictured m
Figure 17: C
A basis pac the forward loss in the the BRD fo which is th defaults be increased c basis packa
fect is that t Figure 17 mium falls, a mature in 10
Changes in t
ckage holde d CDS. Th
event of an or different he same as a efore the eff carry) if the age quickly
the orward C shows that assuming th
years).
he CDS prem
er, however hus while th n un-hedged
forward CD a vanilla CD fective date e bond matu y decreases b
CDS contra t as k, the ef he final mat
mium for forw
r, must assu he net carry d default dom
DS contract DS. In eac of the forw ures or defau
bellow zero
29
acts with late ffective date turity date o
ward CDS co
me the cred y on a basis minates the t options.
ch case, the ward CDS, b ults after the o as the effe
er effective e of the con of the contra
ontracts
dit risk on th package wi
gain off the The base ca returns are but positive e effective d
ctive date is
dates have tract, becom act is unchan
he bond unt ith forward e carry. Fi ase is a 0x1
highly nega and slightly date. The s extended.
lower the c mes further nged (all co
til the effect CDS is incr igure 18 bel 0 year forw ative if the b y higher (du expected re
credit distant, the ontracts
tive date of reased, the llow shows ward CDS,
bond ue to the eturn on the
Figure 18: B
While usin basis packa negative sl are based o can be com estimated r quickly the will be trem
Basis pack the credit q effective d More impo
BRD for CWL
ng forward C ages are the lope, forwar on the condi mparatively recovery rat e loss will b mendous.
kages utilizin quality of th date of the F ortant, if the
LN with Forw
CDS on the e same. In rd CDS redu itional marg
small. Gi tes, the astu be minimal,
ng forward he reference FCDS, using e investor ha
ward CDS
Cable & W n cases of ex
uce the carr ginal defaul iven that bo ute trader co
while if it d
CDS can al e entity. If g an FCDS g
as some con
30
Wireless bas xtreme cred ry on the tra lt probabilit nd prices on ould purchas defaults afte
lso be usefu f an investor greatly incr ntrol over th
is package m it risk, wher ade significa ties, which,
n extreme ri se a bond w er the effect
ul if the inve r is sure the reases the ca
he timing of
may not be re the credit antly. For
in the case isk names c with the expe
tive date of
estor has in e firm will n ash flow on f the default
a good idea t curve has rward CDS of steep cre can hover at ectation if it the FCDS,
side inform not default b
the basis p t of the refe
a, not all an extreme premiums edit curves t or around t defaults
the gain
mation on before the
ackage.
erence
entity, grea The next se
Section 6
The pay-ou finance lite refinancing credit defa this section scenarios a predatory b
At the mos of lenders.
or liquidati CDS contr raising the contract on loan issuan
The key fa refinanced CDS pricin
at profits ca ection deals
6: How CD
uts and strat erature. A g or liquidat ault swaps ar n I briefly d as illustratio
behavior an
st fundamen When ch ing a loan, a racts lower’
liquidation n an ex ante nce on an ex
actor in this , or liquidat ng and impl
an be achiev s directly w
DS Chan
tegies for le A creditors o tion and his re fundame discuss how
ons of this c nd the affect
ntal level, cr hoosing the
and make th s lenders pa n payoff if th e basis, and
x post basis.
equation is ted. Every lied surviva
ved by ‘guid ith this kind
ge the Ru
enders and b optimal cont
s beliefs abo ntally chang
CDS affect change. I foc
t of changin
redit default optimal deb heir contrac ayoffs if it c he firm defa
changes the .
that it is wi ything discu al probabilit
31
ding’ the de d of manipu
ules of the
bond holder tract is base out the lend ging the rel t this relatio cus primaril ng capital str
t swaps are bt contract, ct decision b choose to re aults. By d e lenders de
ithin the len ussed in the ies, has assu
fault past th ulations.
e Game
rs are relativ ed on his inf der’s reactio
lationship b onship broad
ly on the ba ructures on
changing th lenders esti based on the efinance a po
definition th ecision if CD
nder’s powe previous se umed that d
he effective
vely well de formation se n set. As etween cred dest sense. I asis trade, in basis holde
he optimal c imate their p ese factors.
oorly perfor his changes DS contract
er to decide ections up to default timin
date on the
efined in rec et, payouts a hedging in ditor and de
I use severa ncluding hed ers.
contracting payoffs on r The prem rming firm, the lender’
ts are entere
if the firm o this point, ng is indepe
e FCDS.
cent on
nstrument, ebtor. In
al different dging,
decisions refinancing mium on
, while s optimal ed into after
is
, including endent and r
beyond the literature.
Scenario 1
In this scen
“senior sec forms of de the loan is not have su capital mar
I analyze th renegotiati
e influence o