Correlation of default

Transcription

1 efaul Correlaon

2 Correlaon of defaul If Oblgor A s cred qualy deeroraes, how well does he cred qualy of Oblgor B correlae o Oblgor A? Some emprcal observaons are efaul correlaons are general low hough hey decrease as rangs ncrease. efaul correlaons generally ncrease nally wh me and hen decrease as he horzon exends longer. efaul among and beween specfc ndusres are nconclusve.

3 Formula for correlaon of defaul j EF EF j EF EF EF j j EF j where he jon probably of defaul j EF + EFj + j and + j s he probably ha a leas one oblgor has defauled.

4 EF EF + EF EF EF EF Example Suppose EF 5% frm has a 5% probably of defaul, and EF %. If 0 ndependence of defauls, hen jon defaul probably of boh frms 5% % 0.05%. If 0., hen 0.48%. Ths s almos 0 mes as he case of 0.

5 Evaluaon of a leer of cred LOC - backed deb Curren rang agency s o rae LOC-backed deb wh he same cred qualy as he LOC bank. Two falures have o occur before he debholder experences a fnancal loss. Le EF LOC 0.5% and EF oblgor.0%. If 0., hen defaul probably of he LOC-backed deb 0.%. If 0, hen he jon defaul probably s only 0.06%.

6 Esmaon of defaul correlaon.. 3. Use hsorcal defaul daa and sascally calculae parwse correlaon of defaul. Use Mone Carlo smulaon on a specfc choce of rsky deb model and compue he covarance srucure. Gven wo oblgors asse volales and her varance covarance srucure, calculae analycally her jon probably of defaul and compue he defaul correlaon.

7 ffcules n usng hsorcal daa n esmang defaul correlaons. There are no enough me-seres daa avalable o accuraely esmae defaul correlaons.. o no use frm-specfc nformaon. 3. efaul correlaons are me-varyng, so pas hsory may no reflec he curren realy.

8 Smpler mehod of calculang correlaon of defaul Assume ha each defaul probably dsrbuon s normal so ha j s jonly bvarae normal. Le he asse correlaon beween Asse A and Asse B be 0.9; and assume EF a and EF b 0.005, asse volales are σ a 0.5 and σ b 0.6. Jon defaul probably dx dy y xy x b b a a b a b a exp J + σ σ σ σ σ πσ

9 The upper lms a and b are gven by nverse normals, gvng J a 0.75 and b.404, efaul correlaon beween A and B EF a J EF EF a a EF EF b b EF b The calculaed defaul correlaon s sgnfcanly smaller han he asse correlaon.

10 Asse based approach for defaul correlaon Frs passage me model d d lnv lnv µ d µ d + Ω d µ and µ are consan drf erms and are wo ndependen sandard Brownan moons. ' σ σσ ΩΩ σσ σ λ V > e K,,, as he non-defaul requremens.

11 Assumng λ µ avodng he drf erms, hou* 00 obaned r I r I n n e r n n n r 4 4 sn 0 0 0,3,5 4 / 0 0 α π α π α πθ π where I v z s he modfed Bessel funcon wh order b σ υ, + < + > oherwse an 0 f an oherwse an 0 f an π α π θ * An analyss of defaul correlaons and mulple defauls, Rev. of Fn. Sud. Vol. 4, p

12 Le N K V σ τ,0 ln * efaul correlaon beween frm and frm over [0, ] corr, ] [ ] [ ] [ ] [ ] [ + + where + probably ha a leas one defaul has occurred.

13 ynamc naure of defaul correlaon. The defaul correlaon and he underlyng asse reurn correlaon have he same sgn. In general, he defaul correlaon s lower han he underlyng asse reurn correlaon. * Frms n he same ndusry regon ofen have hgher defaul correlaons.. efaul correlaons are generally very small over shor nvesmen horzons. They ncrease and hen slowly decrease wh me. The me o reach he peak defaul correlaon depends on he cred qualy of he underlyng frms.

14 Relaon beween defaul correlaon and me for varous cred quales

15 Over a shor nvesmen horzon, defaul correlaons are low because quck defauls are rare and are almos dosyncrac pecular o ha frm. Over a long me horzon, he defaul of a frm s vrually nevable [non-defaul evens become rare and dosyncrac].

16 Rsk managemen mplcaons. For long-erm nvesmens say, 5 o 0 years, he defaul correlaon can be que a sgnfcan facor f he underlyng frm values are hghly correlaed.. The dynamc naure of defaul correlaons requres acve managemen of he porfolo. Accordngly, he capal requremens mus be adjused hroughou me. For example, f he defaul probably of each loan doubles, he probably of mulple defauls n a porfolo may be sgnfcanly more han doubled.

17 efaul correlaons n dfferen secors of he US 00 US All Ules Transporaon Energy Inv grade NIG Inv grade NIG Inv grade NIG Inv grade NIG One year Inv grade NIG Fve years Inv grade NIG Seven years Inv grade NIG