CVA calculation for CDS on super senior ABS CDO

Transcription

1 MPRA Munich Personal RePEc Archive CVA calculaion for CDS on super senior AS CDO Hui Li Augus 28 Online a hp://mpra.ub.uni-muenchen.de/17945/ MPRA Paper No , posed 19. Ocober 29 13:33 UC

2 CVA calculaion for CDS on super senior AS CDO Hui Li 1 Augus 28 ASRAC he way monoline insurers esimae he FAS 157 credi value adjusmens (CVA) on heir AS CDO insurance porfolios vasly oversaes he benefis. We propose a simple mehod ha is more accurae, especially when he counerpary defaul risk is high. he counerpary defaul recovery rae is also a criical inpu. Counerpary credi risk is an imporan opic oday wih credi crunch affecing increasing number of financial firms. Firms holding super senior piece of AS CDO would normally hedge heir posiion wih a monoline insurer in he form of credi defaul swap (CDS). Under he sress marke condiions for monoline insurers, he effeciveness of he hedge has o be reevaluaed based on he credi qualiy of he counerpary. Credi value adjusmen (CVA) is precisely he measuremen of counerpary credi risk on OC derivaive ransacions. Under he new FAS 157 requiremen, counerparies can also adjus heir liabiliies based on heir own credi qualiy, which leads o he CVA benefis shown on monoline insurers quarerly repors when heir credi spreads widened a lo due o downgrading below AAA raing. In he usual framework for credi value adjusmen calculaion, poenial fuure exposure has o be simulaed before he adjusmen can be calculaed (see reference [1]). Wih all he srucural complexiies of AS CDOs, i is no realisic o carry ou he simulaion in order o calculae CVA. One simple way people would use is o adjus he discoun rae curve by he counerpary CDS spread curve. his mehod is reasonable only when he counerpary CDS spread is small. I is he marke convenion o quoe spread for IG names, bu quoe price for HY names, because using CDS spread adjused discoun curve is no longer accurae for HY names. he recen mind boggling resuls of monoline insurers quarerly repors on CVA benefis have proven ha his simple mehod has o be improved for sressed counerparies. Here we propose a simplified approach wih reasonable accuracy even for sressed names, which will make he calculaion easy o implemen in he AS CDO valuaion frame work. We make a few assumpions abou he model as follows. Firs, mos of he CDS negaive basis rades on super senior CDOs were enered a very low spread, which will have a negaive mark-o-marke value for he proecion seller in he foreseeable fuure. So he counerpary risk will be unilaeral on he proecion seller, or he monoline insurers. Second, we assume he credi qualiy of he counerpary is independen of he AS CDO collaeral performance. In realiy, his assumpion is no necessarily rue, in he ligh of he fac ha monoline insurers have been dragged down by he MM losses 1 hui.li@aig.com. he views expressed are he auhor s own, no hose of AIG.

3 due o heir subprime exposures. Assuming all he sress has already been refleced in he CDS spread curves, his is sill reasonable. hird, we assume recovery rae R is consan, hus independen of counerpary defaul or marke condiions. his is currenly he sandard marke pracice, especially R is normally se o 4%. Under hese hree assumpions, he sandard formula for CVA (see reference [1]) is where CVA = ( 1 R) E dpd(, (1) E is he risk-neural discouned expeced exposure given by Q E = E [ ] (2) where is he ne presen value of fuure cash flows valued a ime and is independen of counerpary defaul, is he fuure value of one uni of base currency invesed in he money marke accoun. PD(, is he risk-neural probabiliy of counerpary defaul beween ime and wih PD (,) =. PD(, can be calibraed from he erm srucure of counerpary CDS spreads. he calibraion is based on he assumpion of 4% recovery rae for corporae bond. Normally firms would have a cash flow model or a correlaion model o value heir AS CDO insurance porfolio. We assume essenially E is he sum of risk-neural discouned expeced fuure cash flows a or afer ime under he CDS conrac. So de is he risk-neural discouned value of he expeced cash flow a ime. We have CVA E PD(, PD(, ( de ) (1 PS(, )( de ) E) (1 R) (1 R) PD(, de PS(, ( de ) (3) where we choose o be slighly afer he mauriy of he deal so ha he exposure a will always be zero, and PS(, is he survival probabiliy beween ime and ime wih PS(, = 1 PD(,. E) is he curren value of he AS CDO insurance porfolio wihou counerpary defaul risk.

4 An inuiive way o undersand equaion (3) is o separae he fuure cash flows ino wo pars, he loss and he recovery. he recovery par will be independen of counerpary defaul risk, while he loss par is coningen on counerpary defaul before he ime of he fuure cash flows. One easy way o implemen he CVA calculaion is o muliply he discoun facors by ( 1 R) * PD(, and rerun he CDS on AS CDO valuaion. o faciliae he calculaion, i is required o separae discoun curve from he forward Libor rae calculaion. Unlike he ineres rae swaps, credi defaul swaps could erminae earlier when here is a credi even. In fac, here are several forms of CDS conracs: cash selemen, physical selemen and Pay-As-You-Go. he firs wo will erminae when credi even happens, bu he laer has he same mauriy as he underlying AS/CDO bond. Monoline insurers normally have he Pay-As-You-Go selemen on heir insurance conracs. he mehod described above is suiable for his case. Since he iming of credi even could be scenario dependen and he counerpary risk no longer exiss afer selemen of defaul loss, he above framework has o be expanded o handle he firs wo cases. Assume for a scenario he credi even happens a ime scenario is calculaed as follows, hen he CVA for ha CVA dpd(, ) PD(, ) (1 R) PD(, d( ) (4) Assume C(, is he cumulaive cash flow from ime o ime. hen = dc(, s) = dc(, s) s s and CVA PD(, ) ) (1 R)( dc(, + (1 R) PS(, dc(, + PD(, PS(, dc(, ) (5) dc(, ) his suggess ha, for ha scenario, he defaul probabiliy curve should be se o consan afer he credi even and hen be muliplied o he discoun curve. So we have o make he adjusmen o discoun curve based on he iming of credi even in each scenario. he final CVA value will be he average over all scenarios. he mehod currenly used by he monoline insurers is equivalen o seing he recovery rae o zero when calibraing he CDS defaul probabiliy and calculaing he CVA. he marke sandard recovery rae assumpion is 4% when quoing he CDS spreads. When (6)

5 CDS spreads are no high, CVA valuaion is no very sensiive o he recovery rae assumpion. However, when CDS spreads are wide, he recovery rae assumpion is very imporan. A quick numerical evaluaion on a sample porfolio of AS CDO insurance porfolio reveals ha, when counerpary CDS spreads are high (over 2bps), which is ypical for he monoline insurers, he difference beween he wo mehods (recovery rae % vs 4%) is huge (mosly over 1%). Of course, acual resuls may vary depending on he underlying CDO porfolios. u i is safe o say ha he monoline insurers quarerly resuls are hugely oversaed compared wih using 4% recovery rae. efore making any conclusion, we would like o review he assumpions underlying our mehod and see if hey need revision o be more precise. he assumpion of negaive poenial fuure exposures for he CDS insurance on super senior AS CDO is reasonable, since he insurance premium is so low ha marke spread will no be lower in foreseeable fuure. he raionale is ha if he premium on he deal is very low hen he mehod can be used. Nex, as menioned before, he assumpion of independence beween counerpary defaul and he CDS valuaion is quesionable. For single name CDS, here is discussion in he lieraure on how o add correlaion o CVA calculaion (see reference [2]). In he case of AS CDO affeced by he morgage crisis, we can assume he correlaion is hrough a sysemaic facor, like he housing price appreciaion (HPA). If he CDO valuaion is driven by HPA scenarios imbedded in a cash flow model, his should no be difficul o implemen. he hird assumpion is also debaable. Research on hisorical daa suggess recovery rae is negaively correlaed wih defaul rae. Recen work has also demonsraed ha sochasic recovery rae model migh be helpful for calibraing he Gaussian copula model on he super senior ranches of CDX and iraxx indices (see reference [3]). I is also arguable o use he same recovery rae for boh corporae bonds and OC derivaive conracs. In his noe, we showed a more accurae mehod o calculae CVA for CDS on super senior AS CDO, especially for sressed counerparies. he way is o adjus he discoun curve by counerpary defaul probabiliy muliplied by he loss given defaul. he key poin is ha, when counerpary credi spread is wide, CVA calculaion is very sensiive o recovery rae assumpion. Adjusing he discoun curve by he counerpary credi spread curve is equivalen o assuming zero recovery rae, which could vasly oversae he CVA benefis for sressed counerparies. he fair value CVA benefis repored by he monoline insurers in heir quarerly repors should be aken wih a grain of sal. References [1] M. Pykhin and S. Zhu, A Guide o Modeling Counerpary Credi Risk, GARP Risk Review, July/Augus 27 Issue 37 p16; [2] D. rigo and K. Chourdakis, Counerpary Risk for Credi Defaul Swaps: Impac of spread volailiy and defaul correlaion, FichSoluions, May 28; [3] S. Amraoui and S. Hiier, Opimal Sochasic Recovery for ase Correlaion, June 28.