Upload
sybil-norris
View
214
Download
1
Tags:
Embed Size (px)
Citation preview
Assessing the effects of collaterals and Assessing the effects of collaterals and guarantee on loan pricing under the IRB guarantee on loan pricing under the IRB approach: a comparative-static analysisapproach: a comparative-static analysis
R. De Lisa*, M. Marchesi**, F. Vallascas*, S. Zedda*R. De Lisa*, M. Marchesi**, F. Vallascas*, S. Zedda*
2007 Small business banking and 2007 Small business banking and financing:financing:a global perspective a global perspective Cagliari,Cagliari, 25th May, 2007 25th May, 2007
*: University of Cagliari (Economics of Financial Intermediaries; Financial Mathematics)*: University of Cagliari (Economics of Financial Intermediaries; Financial Mathematics)
**: European Commission, Dg Internal Market**: European Commission, Dg Internal Market
22
Directive on capital adequacy of Directive on capital adequacy of credit institutions (2006)credit institutions (2006)
New regulation on the treatment of capital New regulation on the treatment of capital adequacy:adequacy:
a)a) risk-sensitive capital adequacy;risk-sensitive capital adequacy;
b)b) Fully recognition of “mitigation techniques” (as Fully recognition of “mitigation techniques” (as collaterals and guarantees – C&G) . collaterals and guarantees – C&G) .
Lower loan overall credit risk Lower level of own Lower loan overall credit risk Lower level of own fundsfunds
33
Loan pricing and C&GLoan pricing and C&G
If the banks’ criteria is based upon the If the banks’ criteria is based upon the evaluation of credit risk components, C&G evaluation of credit risk components, C&G topic becomes relevant.topic becomes relevant.
Micro perspectiveMicro perspective: C&G as a sort of “regulatory : C&G as a sort of “regulatory driver” than can be used in the pricing driver” than can be used in the pricing negotiation process.negotiation process.
Macro perspectiveMacro perspective: C&G could have : C&G could have implications on the overall allocative efficiency implications on the overall allocative efficiency of the credit industry.of the credit industry.
Thus, it is worth to assess the impact of C&G Thus, it is worth to assess the impact of C&G on loan pricing.on loan pricing.
44
The aim of the paper The aim of the paper
The paper aims at providing a quantitative The paper aims at providing a quantitative assessment of the impacts of C&G on a loan assessment of the impacts of C&G on a loan pricingpricing
A comparative-static analysis applied to a A comparative-static analysis applied to a pricing model*. pricing model*.
Pricing model is defined by following Pricing model is defined by following Loan Loan arbitrage-free pricing modelsarbitrage-free pricing models (LAFP). (LAFP). Dermine (1996)Dermine (1996)
*: Under Internal rating based approach.*: Under Internal rating based approach.
55
Methodology: pricing functionMethodology: pricing function
jj
jjddjdejjjddj LGDPD
LGDPDiicopirCLGDPDiiiSpread
1
jj
j
jj
dej
jj
djjdj
LGDPD
cop
LGDPD
irC
LGDPD
iLGDPDiiSpread
111
1
Expected loss component
Unexpected loss component
Organizational component
66
Methodology: Modelling the impact Methodology: Modelling the impact of collateralsof collaterals
jj
j
jj
dej
jj
djj
LGDPD
cop
LGDPD
irC
LGDPD
iLGDPDSpread
111
1
LGD C
77
Methodology: Modelling the impact Methodology: Modelling the impact of guaranteesof guarantees
jj
j
jj
dej
jj
djj
LGDPD
cop
LGDPD
irC
LGDPD
iLGDPDSpread
111
1
PD C
88
Methodology: pricing modelMethodology: pricing model
\
0,5 0,5
1
10,999
11
1 1,5 1 2,5 1,06
jj j j j j
jj
j j j
RC LGD N G PD G PD LGD
RR
b M b
cumulative distribution function for a standard normal random variable
G (x)
N (x)
inverse cumulative distribution function for a standard normal random variable
45/5104,0
501/501124,0501/50112,0
S
EXPPDEXPEXPPDEXPR
correlation proxy
2
0.11852 0.05478j jb Log PD maturity adjustment
jM effective maturity
99
Methodology: pricing modelMethodology: pricing model
(1)
****
*
**
**
111
1
jj
j
jj
dej
jj
djj
LGDPD
cop
LGDPD
irC
LGDPD
iLGDPDSpread
(2) GDJ PDPDPD 1*
0
(3)
E
MVCEMAXLGDJ %45;0*
%450 *LGD 0MVC
(4) 06,15,215,11999,01
1 1*5,0
5,0**
bMbLGDPDG
R
RPDGRNLGDC j
1010
Methodology: limitsMethodology: limits
1) The analysis is based on a “technical” 1) The analysis is based on a “technical” spreadspread
06,15,215,11999,01
1 1*5,0
5,0**
bMbLGDPDG
R
RPDGRNLGDC j
****
*
**
**
111
1
jj
j
jj
dej
jj
djj
LGDPD
cop
LGDPD
irC
LGDPD
iLGDPDSpread
2) C* is the “minimum capital required”2) C* is the “minimum capital required”
1111
Methodology: comparative-static Methodology: comparative-static analysisanalysis
The pricing function
Elasticities of credit spread with respect to PD and LGD
Elasticities of capital requirement with respect to LGD and PD
Elasticities of credit spread with respect to MVC and
In particulary, we considered:
1212
Main results (01)Main results (01)
0,00%
10,00%
20,00%
30,00%
40,00%
50,00%
60,00%
70,00%
80,00%
90,00%
100,00%
0,03% 0,15% 0,45% 0,70% 1,00% 1,40% 2,00% 4,00% 8,00%
PD (%)
%
Expected Loss Unexpected Loss Organizational components
1313
Main results (02)Main results (02)
Elasticities of credit spread with respect to PD and LGD
0.02 0.04 0.06 0.08Pd
0.1
0.2
0.3
0.4
0.5
0.6
spread, LGD
spread, PD
1414
Main results (03)Main results (03)
Elasticities of capital requirement with respect to LGD and PD
C, LGD
C, PD
0.02 0.04 0.06 0.08PDd
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1515
Main results (04)Main results (04)
Elasticities of credit spread with respect to MVC and (given a guarantor’s PD of 0,03% and borrower’s PD of 1,4%)
0.2 0.4 0.6 0.8 1alpha, mvc
-0.4
-0.3
-0.2
-0.1
spread,
spread, MVC
1616
Main results (04)Main results (04)
0.2 0.4 0.6 0.8 1alpha, mvc
-0.4
-0.3
-0.2
-0.1
spread,
spread, MVC
Elasticities of credit spread with respect to MVC and (given a guarantor’s PD of 0,15% and borrower’s PD of 1,4%)
1717
Main conclusionsMain conclusions
1. Collaterals are the strongest mitigation tool1. Collaterals are the strongest mitigation tool1.1. more evident when borrower’s PD 1.1. more evident when borrower’s PD is high is high
No neutral regulationNo neutral regulation
2. Credit spreads are more elastic to C&G than 2. Credit spreads are more elastic to C&G than borrower’s rating improvementsborrower’s rating improvements
2.1. great appeal in releasing C&G, less in upgrading rating class2.1. great appeal in releasing C&G, less in upgrading rating class
2.2. likely impacts on allocative efficiency2.2. likely impacts on allocative efficiency
1818
Further research issues:Further research issues:
A) Modelling bank and firm behaviourA) Modelling bank and firm behaviour
1.1. BankBank::
- economic capital vs. regulatory capital- economic capital vs. regulatory capital
2.2. FirmFirm::
- cost of alternative choices- cost of alternative choices
B) Modelling the impact guarantees under the B) Modelling the impact guarantees under the double default approachdouble default approach
1919
Thanks,Thanks,
Riccardo De Lisa; Riccardo De Lisa; [email protected]@unica.it
Massimo Marchesi; Massimo Marchesi; [email protected]@cec.eu.int
Francesco Vallascas; Francesco Vallascas; [email protected]@unica.it
Stefano Zedda; Stefano Zedda; [email protected]@unica.it
2020
Methodology: pricing modelMethodology: pricing model
jjjjj PDLGDiPDiME 1111
expected value of the credit at the end of the period
ME
ji
jPD
jLGD
interest rate applied on the j risky loan
probability of default of the j debtor
loss given default on j debtor
2121
Methodology: pricing modelMethodology: pricing model
( ) 1 1 1j d j e jU M C i C r cop
jjjjj PDLGDiPDiME 1111
Posing E(M) = U(M) we have:
jj
jdejjjdj LGDPD
copirCLGDPDii
1
2222
Methodology: pricing modelMethodology: pricing model
overall cash flows out
equity funding (%)
interest rate paid on interbank funding
gross return to shareholders
( ) 1 1 1j d j e jU M C i C r cop
operative costs related to the loan
Cj
U (M)
di
er
jcop