DOUBLE IMPACT. Credit Risk Assessment for Secured Loans. Jean-Paul Laurent ISFA Actuarial School University of Lyon & BNP Paribas

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1 DOUBLE IMPACT Credt Rsk Assessment for Secured Loans Al Chabaane BNP Parbas Jean-Paul Laurent ISFA Actuaral School Unversty of Lyon & BNP Parbas Julen Salomon BNP Parbas Abstract : The quanttatve IRB approach evaluatng regulatory captal provdes a benchmark framework for credt rsk assessment. Nevertheless, the postulated ndependence between default events and recovery rates seems napproprate for secured loans such as mortgage loans. The model we ntroduce s an extenson of the regulatory one and takes nto consderaton correlaton effects between default events and collateral market values. As a result, we show that ths s lkely to augment captal requrements n comparson wth Basel II recommendatons. Keywords: Basel II Agreement, Mortgage Loans, Collateral Value, Recovery Rate, Factor Models, Rsk Measure, Value at Rsk INTERNATIONAL CONFERENCE C.R.E.D.I.T. 003 Vence, -3 Sept. 003 Dependence Modellng for Credt Portfolos 1

2 I. Collateral protecton! Default mechansm Summary! Modellng Default and Collateral Value! Dependence between Defaults & Collateral Values II. Aggregatng mortgage portfolos! Aggregated loss : methodology & computaton! Loss dstrbuton : Monte-Carlo results III. Rsk measure! Rsk measures : Value at Rsk & Expected Shortfall! Captal requrements! Comparson wth Basel II benchmark

3 1. Default Mechansm X : Latent Varable for the th oblgor s : threshold such that P(X <s ) = Default Probablty X and C are correlated random varables C < 1 COLLATERAL TOO SMALL Credt Nomnal: 1 Collateral: C X <s DEFAULT X s NO DEFAULT Loss = 0 Loss = 1 - C C 1 ENOUGH COLLATERAL Loss = 0 Loss 1 ( ) + { X < s } 1 C = 3

4 . Modellng Default Latent Varable and Collateral Value " Modellng latent varable X : One factor structure : = ρ Ψ + 1! Ψ systematc rsk factor, gaussan! Ψ specfc rsk, gaussan..d.! ρ correlaton parameter X ρ Ψ " Modellng Collateral Value C 1 st case: C are determnstc Basel II framework nd case: C are postvely correlated varables. Gven a systematc recovery factor ξ, C are ndependent:! J. Frye (Rsk, 000a), E. Canabarro et al. (Rsk 003) : C are gaussan! M. Pykhtn (Rsk 003), Chabaane, Laurent, Salomon (003) : C are lognormal 4

5 3. Modellng Default Latent Varable and Collateral Value " Modellng dependence between X and C! Low recovery rates assocated wth hgh default rates (Altman, 003).! Dependence structure between Default & Collateral Value: Basel II framework, Canabarro et al (003): no correlaton Frye (003), Pykhtn (003): drven by the same rsk factor Chabaane, Laurent, Salomon (003): drven by two correlated rsk factors Remark: assumng the same rsk factors s lkely to nduce harsh collapse of collateral value when default occurs. Ths strong dependence seems napproprate for retal bankng, especally mortgage portfolo. 5

6 4. Credt portfolo Aggregated Loss " The aggregated loss s the sum of ndvdual losses. Credt 1 Credt Credt n Aggregated loss L for the credt portfolo L = n 1 ( ) { < } X s 1 C = 1 + (n oblgors) " Many approaches may be used to derve the loss dstrbuton:!asymptotc expanson (Gordy, Wlde)!Monte-Carlo Smulaton (ndvdual loss, aggregated loss, )!Fourer nverson technques 6

7 5. Comparson wth Basel II benchmark!collateral volatlty leads to fat tal dstrbuton Portfolo loss dstrbuton (EL = 0,%)!Default/recovery correlaton ncreases losses severty 750 BASEL II (NO volatlty NO correlaton) LOW volatlty - LOW correlaton LOW volatlty - STRONG correlaton STRONG volatlty - STRONG correlaton 300!Expected Loss (EL) s hardly unchanged ,0% 0,1% 0,% 0,3% 0,4% 0,5% 0,6% 0,7% 7

8 6. Rsk Measures : VaR vs ES [ 0,1] The Value at Rsk and the Expected Shortfall for a confdence level α are: VaR ES (L) = nf α P α (L) = E > ( t, P[ L t] α) [ L L VaR (L)] VaR : rsk measure retaned by regulatory authortes α ES : consdered a relable alternatve coherent rsk measure to VaR, snce t s sub-addtve and more conservatve. VaR α (L) ES α (L) = E[L L >VaR(α)] Loss Dstrbuton IRB-approach : bank captal charges match the credt rsk magntude (L for retal & corporate, L-E[L] for mortgage) 8

9 " Basel II Model : VaR gven by: " Default/Collateral Model: 7. VaR computaton! If default/collateral correlaton s unspecfed Monte-Carlo smulaton.! Partcular case : correlaton = 100%, VaR gven by the cabalstc expresson : VaR( α) VaR Basel VaR Basel ( α ) = µ / σ + β Φ Φ 1 β = PD 1 Φ Φ (PD); (1 recovery) 1 ( α) µ ; η σ e µ+σ / βρ e e µ+σ Φ Φ σ / βφ 1 Φ ( α) σ β/ Φ 1 1 µ / σ + β Φ ( α) Φ σ 1 β 1 β µ (PD) ση βρ; σ; η βρ σ " Monte-Carlo Smulaton Results: VaR always greater than Basel II VaR! the hgher the volatlty, the hgher the VaR (PD) + 1 ρ (1 α)! the hgher the default/collateral correlaton, the hgher the VaR 1 ρ Φ 1 9

10 8. VaR result : factors correlaton effect VaR/Var(Basel) Systematc correlaton effect on Value at Rsk 3,5! No volatlty = Basel II volatlty=0% volatlty=5% volatlty=10% volatlty=15% volatlty=40% 1,5 1 0% 10% 0% 30% 40% 50% 60% 70% 80% 90% 100% systematc correlaton! Quas-lnear dependence between VaR and correlaton 10

11 9. VaR results : volatlty effect VaR/VaR(Basel) Collateral Volatlty effect on Value at Rsk 3,0,5! Volatlty ncreases VaR correlaton=0% correlaton=10% correlaton=0% correlaton=50% correlaton=100%,0 1,5 1,0 0% 5% 10% 15% 0% 5% 30% 35% 40% volatlty! Strong default/recovery correlatons mply stronger VaR 11

12 Concluson " Keepng coherence wth Basel II!Factor model for Latent Default Varable!Factor model for Collateral Value!Dependence between Default & Recovery " Some results!collateral volatlty clearly ncreases VaR!Murphy s law: n addton to default, collateral value deprecated!expected Shortfall behaves the same way as VaR!Ablty to splt rsk charge nto credt rsk & market rsk 1

13 References & Acknowledgements The authors wsh to thank Antone Choullou, Chrstan Gouréroux, the Fnancal Models Team at BNP PARIBAS for helpful dscussons. [1] E. Altman, B. Brady, A. Rest, A. Sron, The lnk between default and recovery rates: theory, emprcal evdence and mplcatons, Workng Paper, March 003 [] E. Canabarro, E. Pcoult, T. Wlde, Analytc Methods for Counterparty Rsk, Rsk, Sept [3] A. Chabaane, A. Choullou, J.-P. Laurent, Aggregaton and Credt Rsk Measurement n Retal Bankng, Forthcomng n EIR Conference. [4] R. Frey, A. J. McNel, Dependent Defaults n Models of Portfolo Credt Rsk, To appear n the Journal of Rsk 003. [5] J. Frye, Collateral Damage, Rsk, Aprl 000. [6] J. Frye, Depressng Recoveres, Rsk, November 000. [7] M. Gordy, A rsk-factor Model foundaton for Ratngs-based Bank Captal rules, Journal of Fnancal Intermedaton, July 003. [8] M. Pkhtn, Unexpected Recovery Rsk, Rsk, August 003. [9] O. Vascek, Loan Portfolo Value, Rsk, December