Bond pricing theorems. Bond convexity The mathematical relationship between bond yields and prices.
Relationship Pricing
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Transcript of Relationship Pricing
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\~fae bfjje~eirfdrfki dq d ~eodrfkiq`f|cd~herfig rdarfa
^eodrfkiq`f| \~fafig
Doepdib~kq Hkqqvzdq
Jen~ud~v >
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Fir~kbuarfki
R`e cd~herq ezkoze dib akiquce~q reib rk ne ck~eebuadreb/ fizkozeb * bfqae~ifig=
R~dbfrfkido akiae|rq okqe ~eoezdiae * ck~e auqrkce~#k~feireb cd~herfig akiae|rq d~e dbk|reb)
^eodrfkiq`f| Cd~herfig=
r`e ec|`dqfq fq ki= ~eodrfkiq/ curudofrv * fire~darfki
^eodrfkiq`f| \~fafig=
kie kj r`e ckqr |~kcfieir d||ofadrfkiq * rkkoq jk~
d ~eodrfkiq`f| cd~herfig d||~kda`
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R`e k~fgfiq
\~fae Bfjje~eirfdrfki=
w`ei qdoeq kjfbeirfado gkkbq+qe~zfaeq d~e r~diqdareb drbfjje~eir |~faeq j~kc r`e qdce |~kzfbe~)
\~fae Bfjje~eirfdrfki * ^eodrfkiq`f| Cd~herfig=w`ei |~fae bfjje~eirfdrfki rdarfaq/ ~dreq k~ ~digeq d~eakcnfieb k~ ndqeb ki auqrkce~q ndahg~kuib `fqrk~v fi re~cqkj~eodrfkiq`f|/ okvdorv* q`d~fig)
\~fiaf|oe=
d ~eodrfkiq`f|#ndqeb akc|div q`kuob ikr a`d~ge eze~vkiewfr` r`e qdce dze~dge |~fae)
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^eodrfkiq`f| \~fafig
Akibfrfkiq * R~dfrq=
Zfqfki= Okig#Re~c k~feirdrfki
Qak|e= \~kjfrdnfofrv ZQ \~kjfrq
Ec|`dqfq= ^ereirfki ZQ Datufqfrfki
Nd~~fe~q * \~e~etufqfreq=
Bdrd= zdofb/ dbetudre/ |~eafqe/ |e~qkidofqeb
Qegceirdrfki *Dirfaf|drfki= drr~darfzeieqq * |kreirfdo
Akccuifadrfki= auqrkce~q q`kuob ne ebuadreb/ tudofjfeb* |~e|d~eb rk daae|r r`e bfjje~eirfdreb kjje~figq
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Fc|oeceirdrfki * Epdc|oeq
R`e~e d~e qeze~do epdc|oeq kj d||ofeb ~eodrfkiq`f| |~fafigwfr`fi r`e G~eeh qe~zfaeq cd~her=
Ndihfig Fibuqr~v=
f)e) ndihq gfze rk auqrkce~q r`e dnfofrv rk jfidiae d ck~rgdge dr d okwe~~dre ndqeb ki r`ef~ nuqfieqq ~eodrfkiq`f|)
@kreo Rku~fqc Fibuqr~v=
f)e) G~eakreo @kreo a`dfi k~ Aoun @kreo Adqfik Okur~dhf bfjje~eirfdrer`ef~ kjje~figq ndqeb ki r`e ~eodrfkiq`f| kj r`e auqrkce~=
Aoun Cecne~q`f| Gkob * Qfoze~ Ad~bq q|eafdo#|~faeb * epaouqfze kjje~q
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Fc|oeceirdrfki * Epdc|oeq
Afiecd Eire~rdficeir Fibuqr~v=
f)e) Dr`fik~dcdAoun * Kbeki AfieJ~feibq d~e |~kg~dcq r`drkjje~ rk r`ef~ okvdo cecne~q d wfbe ~dige kj nkr`
bfjje~eirfdreb |~fafig kjje~figq * kr`e~ epaouqfze qe~zfaeq)
Kbeki Afiecd R`edr~eq \~fafig \kofav=
CECNE^Q GUEQRQ
Dze~dge \~fae 0 6
Bfqakuir
ndqeb ki iucne~ kj Gueqrq
kie 2/5rfaher jk~ eze~v
1 qa~eeifigq
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Fc|oeceirdrfki * Epdc|oeq
Q|k~rq Eire~rdficeir Fibuqr~v=
f)e) Kovc|fdakq J)A) `vn~fb ~eodrfkiq`f| |~fafig ckbeo jk~r`e redcq qedqkido rfaherq)
GDRE \~fae jk~ ^eiewdoq
(&
Dze~dge \~fae jk~
Iew (&
2/5/:/>4 1/0/6/46/>< 10< 2
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^N\= r`e Bvidcfa D||~kda`
R`e cdmk~frv kj d||ofadrfkiq * darfkiq d~e |d~rq kj dgeie~fa okvdo |~kg~dc k~ qa`ece)
^edoov jew akc|difeq d||ov * fizeqr ki dbzdiaeb/
|u~e * bfqae~ifnoe ~eodrfkiq`f| |~fafig ckbeoq)
R`e iew eakikcfa eizf~kiceir ikr kiov eiaku~dgeqnur becdibq d iew/ ck~e bvidcfa/ zfzfb *dbmuqrfig d||~kda` kj ~eodrfkiq`f| |~fafig=
akirfiukuq |~kg~dccfig jk~ a~edrfig k|rfcdo ^N\kjje~figq8 d qe~feq kjdbmuqrfig bfqakuirq ndqeb kiauqrkce~q reiu~e)
^N\
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^N\= r`e Bvidcfa D||~kda`
\~eakibfrfkiq=Bdrd= d wfbe/ |~eafqe/ cedqu~dnoe * darfkidnoe bdrdndqe jk~
|dqr/ epfqrfig * kigkfig qfrudrfkiq fq ieaeqqd~v)
Qegceirdrfki * Ezdoudrfki= r`e beafqfki ~eodreb rk w`fa`
auqrkce~q d~e drr~darfze * w`v (a~fre~fd& cuqr ne ejjfafeir)
Akc|kieirq=4) di fireg~dreb qvqrec jk~ aodqqfjvfig auqrkce~q ndqeb ki
ndahg~kuib r~diqdarfki * zkouce `fqrk~v)
>) d ckbeo rk |k~r~dv r`e ofihnerweei r`e |~fafig *auqrkce~q ckzeceir+cfg~drfki da~kqq okvdorv aouqre~q)
1) d bvidcfa k|rfcf}drfki |~kaeqq jk~ cdidgfig doo r`e|kqqfnoe r~diqdarfkiq tufahov * |~kjfrdnov)
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^N\= r`e Bvidcfa D||~kda`
\~eakibfrfkiq=Bfjjuqfki= ejjearfze akccuifadrfki da~kqq auqrkce~q r`e zdoueq
kj curudofrv/ fire~darfki * |d~rie~q`f|)
Qdrfqjdarfki * Eigdgeceir= auqrkce~q akirfiukuqov kigkfig
qdrfqjdarfki * wfoofigieqq rk cdfirdfi (> bfceiqfkiq kj okvdorv&)\~kjfrdnfofrv= ei`diaeb nkr` r`e epfqrfig * r`e |kreirfdo oezeoq
kj |~kjfrdnfofrv)
\~darfae * Qkjrwd~e Qkourfkiq=
Qeze~do |fkiee~ A^C qe~zfaeq |~kzfbe~q `dze do~edbv bezeok|qkjrwd~e d||ofadrfkiq r`dr jdafofrdre * akizeirfkidof}e ki r`fqd||~kda`)
QuiRea Nuqfieqq Qkourfkiq
]djfi Odnq * Beoo akimkfir
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R`e Adqe
R`e G~eeh Cknfoe Reoeakccuifadrfkiq Cd~her=\~fafig=r`e cdfi dpfq+ndqfq u|ki w`fa` n~dibq akc|ere
Jkauq= n~dibq d~e |~fcd~fov jkauqeb ki auqrkce~ datufqfrfki
R~eib= bue rk r`e eakikcfa ~eaeqqfki r`e cd~her g~kwr` ~dreqd~e beaofifig w`foe r`e |~fae#qeiqfrfzfrv oezeoq d~e fia~edqfig)
Zkbdjkie * Akqckre= Qun}fbf}drfki= d aodqqfa ~ewd~bfig cediq r`dr ~ewd~bq r`e
auqrkce~ diiudoov wfr` d g~dir dckuir kj ckiev)R`e Fifrfdrfze= r`e auqrkce~ fq ikw dnoe rk r~diqje~ r`fq
dckuir rk `fq jfpeb ckir`ov |dvceirq dq d bfqakuir)
^N\ r~dfoq= r`fq kjje~fig adi ne |e~aefzeb dq d odreir+fibf~ear
^N\ ejjk~r/ qfiae ~eodrfkiq`f|+reiu~e bere~cfie r`e qunqfbv)
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Zkbdjkie \kofav
Cknfoe Qe~zfae \~kg~dc Dze~dge Ckir`ov Akqr Akqr djre~ Bfqakuir
Uiofcfreb >5 >5/>/
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A~frfado Didovqfq
R`e k||k~ruifrv=
R`fq fifrfdrfze adi ne beqa~fneb dq r`e fifrfdo qre| rkwd~bq dck~e ~eodrfkiq`f|#b~fzei |~fafig |kofav)
D ~edo k||k~ruifrv jk~ ezkourfki * fireg~drfki `dq r`uqovd~kuqeb)
R`e jdafofrdrk~q=
Nkr` akc|difeq |kqqeqq * `dze daaeqq rk dbetudre *dnuibdir bdrd (|dqr/ |~eqeir * |kreirfdo ne`dzfk~&)
^ereirfki qwfra` fq ikw ieaeqqd~v/ qfiae r`e cd~her q`kwqokw g~kwr` ~dreq)
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Fireg~drfki
R`e K> We adoo fr Jdf~ Bedo epdc|oe=
Noue Qfoze~ Gkob \odrfiuc
bvidcfa akirfiuuc
~eodrfkiq`f| bezeok|ceir
~eq|earfze * |~k|e~ ~ewd~bfig
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