55 dissertation

8/12/2019 55 Dissertation

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UNIVERSITE PARIS 1 PANTHEON-SORBONNE

MASTER 2 MAEF - Spcialit Recherche : MMMEF

CASH FLOW MODEL

Varsha AIN

Rsum :

La modlisation des flux dans le cadre des produits de titrisation cash est fondamentalepour apprhender les risques inhrents aux diffrentes structures.Pour valuer les financements structurs de type CDO ou ABS le dpartement C!S"Credit !uant Studies# de $atixis Paris a dvelopp un mod%le de cash&flo' (as sur lamodlisation des flux selon un 'aterfall spcifi. Cette mthodolo)ie repose sur le conceptd*+xpected Loss , chaque tranche de titrisation se voit attri(uer une notation relative - laperte attendue.L*o(ectif de ce rapport est d*tudier et de dvelopper une mthodolo)ie quantitative denotation des tranches d*ABS et de CDO fonde sur les mcanismes d*allocation des cash&flo's des actifs titriss

Rapport de stage prsent le 15 Septembre 2008.

Jury :

Philippe BI!H Micha"l TOR#MAN $aetitia $E #AINProfesseur - Paris / Directeur de Sta)e Directrice de Sta)e0niversit Paris / $A1232S $A1232S/45&//6 Bd de l*78pital9:4/; PA


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TAB$E OF !ONTENTS

/. ABS1$O?L+D@++$1S ;

;. 1+


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ABSTRA!T

SecuritiGation is more than ust a financial tool. 2t is an important element in risH mana)ement for (anHsallo'in) them to not only remove su(stantial concentrations and values at risH (ut also permits them toacquire securitiGed assets 'ith potential diversification (enefits. ?hen assets are removed from a (anH*s

(alance sheet 'ith a defined recourse or first loss risH the (anH limits its loss exposure to the amount ofrecourse or first loss protection provided (y it. Credit and interest rate risHs are the Hey uncertainties thatconcern domestic lenders. By passin) on these to investors or to third parties 'hen credit enhancementsare involved financial firms are (etter a(le to mana)e their risH exposure.

1he marHet of securitiGation has )ro'n dramatically since its onset a(out three decades a)o 'ith the total

outstandin) issuance of securitiGed assets soon expected to reach 0SI trillion.

Cash flo' modellin) is crucial to securitiGation and is a fundamental part of the credit&ratin) process.Proper cash flo' models have a structure*s priority of payment 'aterfall im(edded in them andtherefore are a(le to allocate all anticipated cash receipts in accordance 'ith the transaction*s le)aldocuments .2t is the only 'ay to dissect accurately the protectionsprovided (y a structure.

1o evaluate securitiGation structures the C!S "Credit !uantitative Study# department of $atixis Parishas developed a 'aterfall tool to rate tranches of cash CDO and ABS transactions. 1he ratin)s assi)ned toeach class of the transaction reflect the assessment of the risH )iven the transaction*s structure creditenhancement and le)al structure.

So here in this paper 'e first )ive a (rief explanation of 'hat securitiGation is actually and some of theimportant terms related to it. 1hen 'e deal 'ith cash flo' modellin).

1he model allo's that the cumulative default rate can follo' Lo)normal distri(ution Binomial+xpansion 1echnique "B+1# FasiceH distri(ution or onte Carlo distri(ution. ?e taHe 'ell into accountthe effect of recovery delays delinquencies seasonin) and prepayment risH on the cash flo'. Also 'e

perform many tri))er tests liHe Over&collateriGation test 2nterest Covera)e test mar)in test cash test etcto Heep the cash flo' close to reality.

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A!%NO&$E#'EMENTS

2 am very )rateful to onsieur ichaJl 1O


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TERMINO$O'(

SECURITIZATION:

Sec)riti*ati+,is a structured financeprocess 'hich involves poolin) and repacHa)in) of cash&flo'

producin) financial assets into securities that are then sold to investors. 7ence the securities 'hich are

the outcome of securitiGation processes are termed asset&(acHed securities"ABS#.SecuritiGation often

utiliGes aspecial purpose vehicle"SPF# "alternatively Hno'n as a special purpose entity SP+M or special

purpose company SPCM# in order to reduce the risH of(anHruptcyand there(y o(tain lo'er interest rates

from potential lenders. A credit derivativeis also )enerally used to chan)e the credit quality of the

underlyin) portfolio so that it 'ill (e accepta(le to the final investors.

STRUTUR!:

Poolin) and transfer , 1he +rii,at+rinitially o'ns the assets en)a)ed in the deal. 1his is typically a

company looHin) to raise capital restructure de(t or other'ise adust its finances. 0nder traditional

corporate finance concepts such a company 'ould have three options to raise ne' capital, a loan(ond

issue or issuance of stocH. 7o'ever stocH offerin)s dilute the o'nership and control of the company

'hile loan or (ond financin) is often prohi(itively expensive due to the credit ratin)of the company and

the associated rise in interestrates.

:
http://en.wikipedia.org/wiki/Structured_financehttp://en.wikipedia.org/wiki/Asset-backed_securityhttp://en.wikipedia.org/wiki/Special_purpose_entityhttp://en.wikipedia.org/wiki/Bankruptcyhttp://en.wikipedia.org/wiki/Credit_derivativehttp://en.wikipedia.org/wiki/Corporate_financehttp://en.wikipedia.org/wiki/Loanhttp://en.wikipedia.org/wiki/Bond_issuehttp://en.wikipedia.org/wiki/Bond_issuehttp://en.wikipedia.org/wiki/Stockhttp://en.wikipedia.org/wiki/Credit_ratinghttp://en.wikipedia.org/wiki/Interesthttp://en.wikipedia.org/wiki/Structured_financehttp://en.wikipedia.org/wiki/Asset-backed_securityhttp://en.wikipedia.org/wiki/Special_purpose_entityhttp://en.wikipedia.org/wiki/Bankruptcyhttp://en.wikipedia.org/wiki/Credit_derivativehttp://en.wikipedia.org/wiki/Corporate_financehttp://en.wikipedia.org/wiki/Loanhttp://en.wikipedia.org/wiki/Bond_issuehttp://en.wikipedia.org/wiki/Bond_issuehttp://en.wikipedia.org/wiki/Stockhttp://en.wikipedia.org/wiki/Credit_ratinghttp://en.wikipedia.org/wiki/Interest


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1he consistently revenue&)eneratin) part of the company may have a much hi)her credit ratin) than the

company as a 'hole. Eor instance a leasin) company may have provided I/4m nominal value of leases

and it 'ill receive a cash flo' over the next five years from these. 2t cannot demand early repayment on

the leases and so cannot )et its money (acH early if required. 2f it could sell the ri)hts to the cash flo's

from the leases to someone else it could transform that income stream into a lump sum today "in effectreceivin) today the present value of a future cash flo'#.

A suita(ly lar)e portfolio of assets is NpooledN and sold to aspecial purpose vehicle"the iss)er# a tax&

exempt company or trust formed for the specific purpose of fundin) the assets. Once the assets are

transferred to the issuer there is normally no recourse to the ori)inator. 1he issuer is N(anHruptcy

remoteN meanin) that if the ori)inator )oes into (anHruptcy the assets of the issuer 'ill not (e

distri(uted to the creditors of the ori)inator.

Iss)a,ce

1o (e a(le to (uy the assets from the ori)inator the issuer SPF issues trada(lesecuritiesto fund the

purchase. 2nvestors purchase the securities either throu)h a private offerin) "tar)etin)institutional

investors# or on the open marHet. 1he performance of the securities is then directly linHed to the

performance of the assets. Credit ratin) a)encies rate the securities 'hich are issued in order to provide

an external perspective on the lia(ilities (ein) created and help the investor maHe a more informed

decision.

1he securities can (e issued 'ith either a fixed interestrate or a floatin) rate. Eixed rate ABS set the

coupon "rate# at the time of issuance in a fashion similar to corporate (onds. Eloatin) rate securitiesmay (e (acHed (y (oth amortiGin) and non&amortiGin) assets. 2n contrast to fixed rate securities the rates

on floaters 'ill periodically adust up or do'n accordin) to a desi)nated index such as a 0.S. 1reasury

rate or more typically the London 2nter(anH Offered


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as protective layers for the A class. 1he senior classes have first claim on the cash that the SPF

receives and the more unior classes only start receivin) repayment after the more senior classes have

repaid. Because of the cascadin) effect (et'een classes this arran)ement is often referred to as a cash

0l+ ater0all. 2n the event that the underlyin) asset pool (ecomes insufficient to maHe payments on the

securities "e.). 'hen loans default 'ithin a portfolio of loan claims# the loss is a(sor(ed first (y thesu(ordinated tranches and the upper&level tranches remain unaffected until the losses exceed the entire

amount of the su(ordinated tranches. 1he senior securities are typically AAA rated si)nifyin) a lo'er

risH 'hile the lo'er&credit quality su(ordinated classes receive a lo'er credit ratin) si)nifyin) a hi)her

risH. 1he most unior class "often called the e)it3 class# is the most exposed to payment risH. 2n some

cases this is a special type of instrument 'hich is retained (y the ori)inator as a potential profit flo'. 2n

some cases the equity class receives no coupon "either fixed or floatin)# (ut only the residual cash flo'

"if any# after all the other classes have (een paid.

2f the underlyin) assets are mort)a)es or loans there are usually t'o separate Nater0allsN (ecause the

principal and interest receipts can (e easily allocated and matched. But if the assets are income&(ased

transactions such as rental deals it is not possi(le to differentiate so easily (et'een ho' much of the

revenue is income and ho' much principal repayment. 2n this case all the income is used to pay the cash

flo's due on the (onds as those cash flo's (ecome due.

Credit enhancements affect credit risH (y providin) more or less protection to promised cash flo's for a

security.

Ser4ici,

A ser4icercollects payments and monitors the assets that are the crux of the structured financial deal.

1he servicer can often (e the ori)inator (ecause the servicer needs very similar expertise as the ori)inator

and 'ould 'ant to ensure that loan repayments are paid to the Special Purpose Fehicle.

1he servicer can si)nificantly affect the cash flo's to the investors (ecause it controls the collection

policy 'hich influences the proceeds collected the char)e&offs and the recoveries on the loans. Any

income remainin) after payments and expenses is usually accumulated to some extent in a reserve or

spread account and any further excess is returned to the seller. Bond ratin) a)encies pu(lish ratin)s of

asset&(acHed securities (ased on the performance of the collateral pool the credit enhancements and the

pro(a(ility of default.

Repa3/e,t str)ct)res

0nliHe corporate (onds most securitiGations area/+rti*e. meanin) that the principal amount (orro'ed

is paid (acH )radually over the specified term of the loan rather than in one lump sum at the maturity of

the loan. Eully amortiGin) securitiGations are )enerally collateraliGed (y fully amortiGin) assets such as

home equity loans auto loans and student loans. Prepa3/e,tuncertainty is an important concern 'ith

9
http://en.wikipedia.org/wiki/Amortizationhttp://en.wikipedia.org/wiki/Amortizationhttp://en.wikipedia.org/wiki/Home_equity_loanhttp://en.wikipedia.org/wiki/Student_loanhttp://en.wikipedia.org/wiki/Amortizationhttp://en.wikipedia.org/wiki/Home_equity_loanhttp://en.wikipedia.org/wiki/Student_loan


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fully amortiGin) ABS. 1he possi(le rate of prepayment varies 'idely 'ith the type of underlyin) asset

poolR so many prepayment models have (een developed in an attempt to define common prepayment

activity. 1he PSA prepa3/e,t /+.elis a 'ell&Hno'n example.

Standard cate)ories of securitiGations are/.mort)a)e&(acHed securities "BS# 'hich are (acHed (y mort)a)esR

6.asset&(acHed securities "ABS# 'hich are mostly (acHed (y consumer de(tR

;.CollateraliGed de(t o(li)ations"CDO# 'hich are mostly (acHed (y corporate (onds or other corporate

de(t.

OERCOLLATERIZATION:

2t is the process of postin) more collateral than is needed to o(tain or secure financin). Over&

collateraliGation is often used as a method of credit enhancement (y lo'erin) the creditorQs exposure to

default risH.

Over&collateraliGation is often done in order to )et a (etter de(t ratin) from a credit ratin) a)ency. 1he

principal underlyin) a pool of assets is often )reater than the principal amount of the issued security (y

approximately /4&64.

Eor example in the case of a mort)a)e (acHed security the principal amount of an issue may (e I/44

million 'hile the principal value of the mort)a)es underlyin) the issue may (e equal to I/64 million.

AMORTIZATION:

/. 1he payin) off of de(t in re)ular instalments over a period of time.

6. 1he deduction of capital expenses over a specific period of time "usually over the assetQs life#. ore

specifically this method measures the consumption of the value of intan)i(le assets such as a patent or a

copyri)ht.

WAC !W"i#$t"d A%"ra#" Cou&on':

1he 'ei)hted&avera)e )ross interest rates of the pool of mort)a)es that underlie a mort)a)e&(acHed

security "BS# at the time the securities 'ere issued. A mort)a)e&(acHed securityQs current ?AC can

differ from its ori)inal ?AC as the underlyin) mort)a)es pay do'n at different speeds. 2n the 'ei)hted&

avera)e calculation the principal (alance of each underlyin) mort)a)e is used as the 'ei)htin) factor.

E(CESS S)READ:


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DELIN*UENT MORT+A+E :

2t is a mort)a)e for 'hich the (orro'er has failed to maHe payments as required in the loan documents. 2f

the (orro'er canQt (rin) the payments current 'ithin a certain time period "transition time# the lender

may initialiGe foreclosure proceedin)s.

Eoreclosure is a last resort for lenders (ecause it is an expensive procedure and lenders typically lose

money in foreclosure proceedin)s. A for(earance a)reement is a potential option to foreclosure if the

(orro'erQs financial difficulties are temporary. A deed in lieu of foreclosure is another option to

foreclosure.

MOOD,-S IDEALIZED CUMULATIE E()ECTED LOSS RATES TA.LE FOR A.S/CDO:


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!HAPTER 1

INTRO#U!TION

Cash flo' modellin) reveals the exact moment of as 'ell as the conditions that 'ould cause a default. 2tnot only serves to allocate funds (ut is also an invalua(le tool to quantify related transaction risHs such asthe effect of any excess spread (et'een assets and lia(ilities prepayment of assets delinquencieson)oin) transaction expenses and the timin) of defaults and recoveries. +ach of these issues is a complexvaria(le. ?ithout a sophisticated model it is difficult to understand their interaction and their ultimatequantifia(le affect on credit quality.

1he cash flo' payments are distri(uted accordin) to rules set forth in the prospectus. +very transaction isunique each structure has its o'n characteristics and contractual possi(ilities are endless.

010 T$is too2 d"%"2o&"d int"#rat"s t3o st"&s:

1he model simulates the distributionof the cumulative default rate usin) one of the four methods"FasiceH B+1 Lo)normal distri(utions or onte Carlo simulations# "#apter $%.

Eor each period it reproduces the cash flo' structure to assess the expected loss on each tranche.

014 Mod"2 out&uts 5or "a6$ 62ass o5 not"s ar":

E5pecte. $+ss

2t is calculated (y 'ei)hin) the loss in each scenario (y the pro(a(ility of occurrence of that scenario.1he loss is determined accordin) to one of the chosen distri(ution.

E5pecte. A4erae $i0e

2t is calculated (y taHin) the ratio of the 'ei)hted sum of principal received over all the periods andsum of principal received over all the periods and then multiplyin) this ratio (y the frequency ofcoupon payment.

Associated !uantitative Rati,(ased on oody*s 2dealised +xpected Loss 1a(le for ABSTCDO.

/4


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#etaile. #e0a)lt Sce,ari+1he N


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R"s"r%" Fund


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!HAPTER 2

&ATERFA$$

410 Wat"r5a22:

?aterfall or priority of payments is a set of contractual terms )overnin) the payout of interest andprincipal on the reference portfolio.1he 'aterfall is a Hey structural feature (ecause it defines the relative stren)th of the various transaction

participants includin) senior su(ordinated and equity investorsR ori)inatorsR and )uarantee providers.1he 'aterfall (alances the various interests (ecause it defines 'ho receives cash flo's. +very dollarallocated to a particular interest is a dollar that is unavaila(le to others. By definition ABS transactionshave a quantifia(le and limited incomin) cash flo' stream. 0nder stress scenarios there 'ill not liHely (e

enou)h resources to cover everyone and the 'aterfall defines 'ho incurs losses.

1he )raph (elo' illustrates a standard cash flo' allocation do'n a capital structure,

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Our 'aterfall model is desi)ned usin) the principle of dou(le entry accountin),A credit to one account causes a de(it to another account. 1his method allo's us to create and modify'aterfall structure very easily.

All 'aterfall instructions are stored in the form of templates 'ith si8 6om&on"nts,

01 Acti+,1his field )ives the instructions descri(in) the amount of funds to (e moved.

41 Pri+rit3

1his field defines the order in 'hich the payment is executed.

71 Test

1his field provides information a(out additional parameters that descri(e the 'aterfall action morespecifically such as a tri))er test.

91 Test res)lt

1his field indicates the required test result to execute the 'aterfall action defined in the 'aterfall*sinstructions.

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1 S+)rce acc+),t

1his field indicates the account 'hich is the repository of funds requirin) to (e distri(uted as per theaction defined in the 'aterfall*s instructions.

;1 #esti,ati+, Acc+),t1his field indicates that account to 'hich the funds are channelled from the source account as per theaction of the 'aterfall

Sample of template,

414 T


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1his )athers t'o su( collateral accounts,

a6 I,terest !+llateral Acc+),t

1his holds interest received from the collateral "interest paid (y the (orro'ers of the loan#

76 Pri,cipal !+llateral Acc+),t1his holds principal received from the collateral "principal paid (y the (orro'ers of the loan#.

Resi.)al Acc+),t

1his is the account 'hich holds the remainin) interest and principal if any after all the paymentshave (een made.

-R !9 TR49!

Pri,cipal Tra,che Acc+),t

1his account receives the principal payment from the principal collateral account.

I,terest Tra,che Acc+),t

1his account receives the interest payment from the interest collateral account.

Fees Acc+),t

1his is the SPF*s account 'hich receives the fees of its services from the ori)inator of thesecuritiGation.

Reser4e Acc+),t

A reser4e acc+),tis created to reim(urse the issuin) trust for losses up to the amount allocated

for the reserve. 1o increase credit support the reserve account can (e replenished throu)hout thelife of the collateral meanin) that the account 'ill increase proportionally up to some specifiedlevel as the outstandin) de(t is paid off.2t can (e used 'hen SPF expenses are )reater than itsincome.

417 A6tions:

Accordin) to the a(ove example of the template 0+r each peri+.the model 'ill execute the follo'in)steps,

A!TION 1 8Fees Pa3/e,t6: 1his action consists in payin) the fees of SPF from the cash collateral

account to the fees account of the SPF.

A!TION 2 8Tra,s0er I,terest A4aila7le6: 1ransfer the interest from collateral account "OTS (alance# tothe interest collateral account of SPF.

A!TION 9 8Tra,s0er Pri,cipal A4aila7le6:1ransfer the principal from collateral account "OTS (alance#to the principal collateral account of SPF.

A!TION 8I,terest Pa3/e,t6:1his consists in payin) the interest due of the period from the SPF*sinterest collateral account to the interest tranche accounts in the descendin) order of the seniority of thetranches .

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A!TION ; 8Pri,cipal Pa3/e,t6:2n the sample template it depends on the mar)in test. 2f the test passesthen Action : is executed 'hich consists in usin) cash availa(le in the cash collateral "Xinterest collateralaccount W principal collateral account# to pay the principal due to tranches on a pro rata (asis "in thedescendin) order of the seniority of the tranches#.

2f the mar)in test fails 'hich means the actual cash is not enou)h to pay all principal due to tranches then,

A6 A!TION < 8Tra,s0er t+tall36:2t consists in transferrin) the reserve cash from the reserve fund to thecash collateral account.

B6 A!TION = 8A/+rtisati+,6: 2t consists in amortiGin) the tranches on a sequential (asis in thedescendin) order of their seniority.

A!TION > 8Reser4e Reple,ish/e,t6:2t consists in transferrin) the remainin) cash"if any# from theinterest collateral account to the reserve fund up to the maximum reserve amount the structure cansupport.

A!TION ? 8Tra,s0er t+tall36: 2t consists in transferrin) the remainin) cash "if any# of the cashcollateral account to the residual interest account used to pay the +quity tranche.

419 )rin6i&a2 )a


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1he term tur(o is meant to (e descriptive in that these structures provide the fastest most acceleratedmeans to repay senior investors.

Conversely the term s"=u"ntia2 reflects the payin) of o(li)ations in full in order of seniority. A priorityof payments 'aterfall that allocates incomin) cash flo's on a&ro rata(asis shares resources and is less

favoura(le to senior investors "and more favoura(le to other transaction parties#. 1he follo'in) is apotential 'aterfall for a pro rata structure,ZCost and EeesZ 2nterest on senior notes.Z 2nterest on unior notes.Z inimum principal on senior notes as defined (y a tar)et amortiGation schedule.Z inimum principal on unior notes as defined (y a tar)et amortiGation schedule.Z


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Class C $otes I9+quity I;

Eor Class A $otes I6:X"I/44&I9:# Eor Class B $otes I/4X"I/44&I9:&I/:# Eor Class C $otes I9X"I/44&I9:&I/:&I9#

- RatioX Par of Assets T Par of Lia(ilities

+xample, Class A OTC ratio X I/44TI9: X /;;.;

- T!ST, 1ests a(ility of the collateral to support outstandin) lia(ilities Compares over&collateriGation ratio to a pre&set threshold

2f OTC


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!HAPTER 9

#ISTRIBUTION OF !UMU$ATIVE #EFAU$T RATE AN# PREPA(MENT

Distribution In&uts

All input parameters re)ardin) the cumulative default rate distri(ution of the portfolio need to (e input inthe NodelN 'orHsheet as displayed (elo',

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3.1Distribution T


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1he +xpected Loss "+L# of the class of notes to (e rated considerin) all possi(le default scenarios is, d+L X ] P +

X /

'here + is the loss of the class of notes to (e rated under scenario

+ is computed as the difference (et'een the nominal value of the class of notes and the net present valueof the cash flo's received (y the note holders assumin) that the assets cumulative default l l W bl M

$o' Hno'in) the expected loss for each note to (e rated "tranche# and the time to maturity "calculated ina similar manner# one can )et the ratin) of that note (y looHin) at the oody*s 2dealiGed +xpected Lossasi"e?@s (1A8% distribution,Let there (e n (orro'ers in a portfolio or 'e can say let there (e a portfolio of n loans 'ith maturity 1.Assume that a loan defaults if the value of the (orro'er*s assets at the loan maturity 1 is less than hisde(t "D# 'ith a pro(a(ility p. Let "4 \ \ /# (e the coefficient of correlation (et'een any t'o

(orro'er*s assets.

Let Ait X Falue of the i th (orro'er*s assets in the portfolio at time t (e descri(ed (y the lo)arithmic?einer process ,

titiitiiti d/0dt0d0 += "/#

?herei is the drift^i is the volatility ?it represents the ?einer "Bro'nian# process.

1he asset value at 1 can (e represented as,

Tiiiiii BTTT0T0 _`

flo)#"lo) ++= "6#

"?e apply 2to lemma on ln"Ai"t#Rt# and inte)rate it (et'een time interval 4 and 1 #

SotT

//0

tiTi

Tti

=

follo's standard normal distri(ution

6;


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X [ ]*6pC


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1he variance s_ X FarL X $6"$&/"p# $&/"p# # j p_ 'here $6 is the (ivariate cumulative normaldistri(ution.

Continuous on the interval 4/M Symmetric i.e E"xRp# X /& E"xRp# ?hen 4 or / the distri(ution concentrates at LX4 or LX/ 0nimodal 'ith the mode at , L modeX $""k"/& #U$&/"p##T "/&6p## 7i)h sHe' and Hurtosis

9 BET:

B+1 method used (y oody*s to rate the securities is the most strai)htfor'ard method of all to estimatethe loss distri(ution of a structured transaction. 2t is comparatively less expensive in terms of money andtime a)ainst the 'ell Hno'n onte Carlo simulation technique.

B+1 method is (ased on the concept of 3i+ersity S"ore "D# 'hich is used to (uild a hypotheticalhomo)eneous pool of independent securities each havin) the same pro(a(ility of default" determined (ythe &eig#ted a+erage probabilityo' de'aultof the ori)inal pool of assets#. Eor any portfolio of assets 'ithD diversity score it is equivalent to consider a portfolio of D assets 'ith DW/ possi(le default scenarios.2f p is the 'ei)hted avera)e pro(a(ility of defaults of the ori)inal portfolio then the pro(a(ility that th "X 4 / 6 D# scenario "P# 'ill occur is )iven (y the (inomial distri(ution,

( ) ( ) =3=

= pp=3=3C

= /UUmmm

?e calculate the DS (y usin) the follo'in) al)orithm,

Let n X $um(er of assets in a sin)le industry of all the industries considered in a pool

f`

`

ffUn

++=

+=

?

n?dds

n?

[ ]dds3S=

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()*

-,%

,%

,%

#,%

#,%

,%

,%

$,%

$,%

,% ,% ,% !,% ",% #,% #,%

Cumulative Default Rate

Probability

()*

Pro(a(ility X / $um(er of assets X /64

1he +xpected Loss "+L# of the note to (e rated considerin) all possi(le default scenarios is, d+L X ] P +

X /

'here + is the loss of the note to (e rated under scenario + is calculated (y taHin) the present value of the cash flo's received (y the note holder assumin) thereare defaults and usin) note coupon as the discount factor. And in the same 'ay as descri(ed inlo)normal technique 'e can find the ratin) of the class of notes.

Since this B+1 method taHes into account all the default scenarios it captures the so called tail effects.

?ith the increase in the diversity score of the portfolio the expected loss decreases,

M+,te-!arl+:

0nliHe FasiceH and B+1 onte&Carlo method can (e applied to almost any type of assets in the portfolioi.e. one can use this technique to evaluate the model even if the portfolio is non&homo)eneous and hasany num(er of assets. But it is expensive (oth in terms of money and computational time.2n this the defaultTno&default state for each asset is simulated (y considerin) the value of a randomvaria(le compared to a default threshold.Consider a portfolio of m assets over a fixed time horiGon 1 3X "3 /3m#1the m&dimensional normalrandom vector 'ith standardiGed one&dimensional mar)inal distri(ution and 'ith associated thresholdslevels x/ .. xm

Let for all i X / . mDi X / if i defaults 4 other'ise R

69


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vi X loss associated to i R


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Eor each type of default distri(ution the user has to specify the respective parameters,

/. $+,+r/al /eth+.

ean and standard deviation of cumulative default rate usually provided in oody*s pre&sales.

2 Vasice /eth+.

Asset correlation and pro(a(ility of default for the considered maturity.

Eor information it is possi(le to compute FasiceH parameters levels directly from Lo)normalparameters "a specific


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security. 1he most (asic metric has a distinctly actuarial name. 2t is called si,le /+,thl3 /+rtalit3

"S#. 2t indicates for any )iven month the fraction of mort)a)esprincipalthat had not prepaid (y the

(e)innin) of the month (ut does prepay durin) the month. Eor computational purposes if a mort)a)e

does prepay in a )iven month its scheduled principal payment for that month is not considered part of the

prepayment.

A related concept is the c+,.iti+,al prepa3/e,t rate"CP


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Scale X /444 corresponds to first default scenario step equal to 4./ and then the default scenarioincreases (y 4./ from one scenario to another.1his field is not necessary 'hen onte&Carlo method is selected.

Mat)rit3of the transaction and payment frequency of assets lia(ilities in order to determine the

num(er of periods.

1Rec+4er3 Rate:1his field is not necessary 'hen onte&Carlo method is selected as recovery rates are set individually for

portfolio entity throu)h the C sheets.

Seas+,i, :

1his field depicts the a)e "in months# 'hen the deal is ready to (e sold in the marHet after the process ofsecuritiGation.

Prepa3/e,t rate:

1. CR (nnual%

2. Crepayment Speed ('or CS%

Prepayment curve,

Prepayment Curve

,%

,%

,%

!,%

",%

#,%

#,%

#,%

#!,%

#",%

,%

# $ & ' ## #$ # #& #' # $ & ' $# $$ $ $& $'

Months

CPR

D"5au2t Timin# distribution (not ne"essary en ) met#od is used%

1his is a vector 'hich specifies 'hat percenta)e of the total default rate 'ill occur in each period oncedefaults start and this vector must add to /44

;6


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1he timin) 'ith 'hich losses occur in the transaction is another important driver of the notes* creditquality. 2ndeed the more losses occur to'ard the end of the transaction the )reater 'ill (e their ne)ativeimpact on the notes* credit quality.

R"6o%"r< Timin# distribution :

1his is a vector 'hich specifies 'hat percenta)e of the recovery rate 'ill occur in each period and thisvector must add to /44.

Eor example,

Let cumulative default rate X 64


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!HAPTER

FORMU$AE

Som" 5ormu2as us"d in bui2din# t$" 6as$ 52o3 3or>s$""t:

-R SS!TS

/. Contractual Amortisationt"supposed to (e linearly calculated#X OTS BOPt"Be)innin) of period# TVPeriod

46. Defaulted AmounttX Cumulative default rateU Default time distri(ution tU Collateral Amount

4;. Delinquent AmounttX Delinquency ultiple U Defaulted AmounttWdelay

4. Prepayment AmounttX ax "4 "OTS BOP j Defaulted Amounttj Delinquent Amountt#U"/&"/&Prepayment


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//. Actual cash receivedtX ax "4 R" Actual Amortisationt W


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;9


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Pr+7le/ 7ei, +re. +,:

?e provide a hypothetical cumulative default distri(ution "expressed in of the ori)inal (alance# to the

cash flo' model (ut if prepayment is important the real cumulative default distri(ution can finally (e

lo'er than the one 'e expected.Eor example,

2f prepayment rate X :: and 'e have cumulative default timin) scenario as (elo',

erio 3e4a5l, *iming 3is,ri65,ion

# 0%

2 0%

$ 20%

0%

%

! 0%& $%

1hen may(e due to a hi)h prepayment rate 'e 'ill not have enou)h collateral amount left in the seventh

period in order to realiGe the default percenta)es of for example ;: 'hich is a very crucial percenta)e

of default.

So the aim here is to correctly stress the hypothetical cumulative default distri(ution in order to )et a real

cumulative default distri(ution equal to the one 'e expected.

2t has (een envisa)ed to do this in three steps,

St"& 0, Eor to calculate the stress factor 'e discretiGe the interval to 'hich the stress factor can (elon)

"'e taHe for example the interval &/ ;4M and then for each value the cumulative default rate is

calculated usin) the formulas as (elo' the cash flo' model is run and then 'e compute the actual

cumulative default rate.

0sedDefaultStress &/;4M R

+

+=

ot#er&isetStressUsed3e'aul

tStressUsed3e'auli'4byear"t3'tSmoot#ing1tStressUsed3e'aul

Stress3't

t

t

/

#4"##Uexp"/"/

'ith "t3'tSmoot#ing1 a parameter "the intensity of the exponential distri(ution#

##/"Prexp"Pr

=Lt3'tRate

3RStress3'tepay1a"torepayStress ttt

'ith PrepayEactor and LtDft


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#/" ttt 3RStress3't)inate0"tual3'tR =

###/"Prexp"

#Pr/"Pr"/"Pr

t

tttt

CRepay"tSmoot#ing1

epayStressepayStressCR)inepayRate0"tual

+=

#Pr/#"/"/ tttt epayRate0"tualate0"tual3'tRal-utollat


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BIB$IO'RAPH(

/. SecuritiGation, 1he Einancial 2nstrument of the Euture Finod >othari Pu(lished (y ?iley Einance

6.'''.fitchratin)s.com+mer)in)&arHet Structured Einance, 0nderstandin) ?aterfalls and Partial@uarantees A // 6449

;. Structured Einance odellin) +van 12C> Pu(lished (y ?iley Einance

. Standard and Poor*s CollateraliGed De(t O(li)ations Septem(er 66 644:

:. CDO C

55 dissertation

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