Transcript Garanzie e pricing - University of Cagliari

Assessing the effects of collaterals and guarantee
on loan pricing under the IRB approach: a
comparative-static analysis
R. De Lisa*, M. Marchesi**, F. Vallascas*, S. Zedda*
2007 Small business banking and financing:
a global perspective
Cagliari, 25th May, 2007
*: University of Cagliari (Economics of Financial Intermediaries; Financial Mathematics)
**: European Commission, Dg Internal Market
Directive on capital adequacy of credit
institutions (2006)
New regulation on the treatment of capital adequacy:
a)
risk-sensitive capital adequacy;
b)
Fully recognition of “mitigation techniques” (as
collaterals and guarantees – C&G) .
Lower loan overall credit risk
Lower level of own funds
2
Loan pricing and C&G
If the banks’ criteria is based upon the evaluation of
credit risk components, C&G topic becomes relevant.
Micro perspective: C&G as a sort of “regulatory
driver” than can be used in the pricing negotiation
process.
Macro perspective: C&G could have implications on
the overall allocative efficiency of the credit industry.
Thus, it is worth to assess the impact of C&G on loan
pricing.
3
The aim of the paper
The paper aims at providing a quantitative
assessment of the impacts of C&G on a loan pricing
A comparative-static analysis applied to a pricing
model*.
Pricing model is defined by following Loan
arbitrage-free pricing models (LAFP). Dermine
(1996)
*: Under Internal rating based approach.
4
Methodology: pricing function
Spread  i j  id 
id  PD j  LGD j  C j  re  id   cop j  id  id  PD j  LGD j
Spread  i j  id 
Expected loss
component
1  PD j  LGD j
PD j  LGD j  1  id 
1  PD j  LGD j

C j  re  id 
1  PD j  LGD j
Unexpected loss
component

cop j
1  PD j  LGD j
Organizational
component
5
Methodology: Modelling the impact of
collaterals
Spread 
PDj  LGDj  1  id 
1  PDj  LGDj
LGD

C j  re  id 
1  PDj  LGDj

copj
1  PDj  LGDj
C
6
Methodology: Modelling the impact of
guarantees
Spread 
PDj  LGDj  1  id 
PD
1  PDj  LGDj

C j  re  id 
1  PDj  LGDj

copj
1  PDj  LGDj
C
7
Methodology: pricing model
0,5



 Rj
1
  G  PD j   
C j   LGD j  N 

 1  Rj
 1  R  
j 




\



0,5


 G  0,999   PD j  LGD j  




1  1,5  bj   1   M j  2,5  bj   1, 06
1
N (x)
cumulative distribution function for a standard normal random variable
G (x)
inverse cumulative distribution function for a standard normal random
variable
R  0,12  1  EXP 50  PD /1  EXP 50  0,24  1  1  EXP 50  PD / 1  EXP 50
 0,04  1  S  5 / 45
correlation proxy

b j  0.11852  0.05478  Log  PD j 
Mj
effective maturity

2
maturity adjustment
8
Methodology: pricing model
PD j  LGD j  1  i d
*
(1)
Spread

*
*

*

*
1  PD j  LGD j
*

cop j

*
1  PD j  LGD j

E  MVC 
LGD*J  MAX 0;45% 

E


(3)
*
*
*
1  PD j  LGD j
PDJ*  1  a  PDD  a  PDG
(2)
(4) C j
C j  re  i d
a 0
0  LGD*  45%
MVC  0
0 ,5






R


0
,
5
*
  LGD  N 1  R   G PD  
  G 0,999   PD  LGD*   1  1,5  b  1  1  M  2,5 b  1,06




1 R 


9
Methodology: limits
1) The analysis is based on a “technical” spread
Spread 
PD*j  LGD*j  1  id 
1  PD*j  LGD*j

C*j  re  id 
1  PD*j  LGD*j

cop j
1  PD*j  LGD*j
2) C* is the “minimum capital required”
0, 5




 R 
0,5
1
*
*
C j   LGD  N 1  R   GPD  
  G0,999  PD  LGD   1  1,5  b   1  M  2,5 b1,06
1 R 




*
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Methodology: comparative-static
analysis
In particulary, we considered:
 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 a
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Main results (01)
100,00%
90,00%
80,00%
70,00%
%
60,00%
50,00%
40,00%
30,00%
20,00%
10,00%
0,00%
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
12
Main results (02)
Elasticities of credit spread with respect to PD and LGD
0.6
0.5
0.4
0.3
0.2
0.1
0.02
0.04
0.06
0.08
Pd
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Main results (03)
Elasticities of capital requirement with respect to LGD and PD
1
0.9
e C, LGD
0.8
0.7
0.6
0.5
e C, PD
0.4
0.3
0.02
0.04
0.06
0.08
PDd
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Main results (04)
Elasticities of credit spread with respect to MVC and a
(given a guarantor’s PD of 0,03% and borrower’s PD of 1,4%)
0.2
0.4
0.6
0.8
1
, mvc
alpha
-0.1
e spread, a
-0.2
-0.3
-0.4
e spread, MVC
15
Main results (04)
Elasticities of credit spread with respect to MVC and a
(given a guarantor’s PD of 0,15% and borrower’s PD of 1,4%)
0.2
-0.1
0.4
0.6
0.8
1
, mvc
alpha
e spread, a
-0.2
-0.3
e spread, MVC
-0.4
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Main conclusions
1. Collaterals are the strongest mitigation tool
1.1. more evident when borrower’s PD is high
2. Credit spreads are more elastic to C&G than
borrower’s rating improvements
2.1. great appeal in releasing C&G, less in upgrading rating class
2.2. likely impacts on allocative efficiency
No neutral regulation
17
Further research issues:
A) Modelling bank and firm behaviour
1. Bank:
- economic capital vs. regulatory capital
2. Firm:
- cost of alternative choices
B) Modelling the impact guarantees under the double
default approach
18
Thanks,
Riccardo De Lisa; [email protected]
Massimo Marchesi; [email protected]
Francesco Vallascas; [email protected]
Stefano Zedda; [email protected]
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Methodology: pricing model


 


E M   1  i j  1  PD j  1  i j  1  LGD j  PD j
EM 
ij
PDj
LGD j
expected value of the credit at the end of the period
interest rate applied on the j risky loan
probability of default of the j debtor
loss given default on j debtor
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Methodology: pricing model


 


E M   1  i j  1  PD j  1  i j  1  LGD j  PD j
U ( M )  1  C j   1  id   C j  1  re   cop j
Posing E(M) = U(M) we have:
ij 
i d  PD j  LGD j  C j  re  i d   cop j
1  PD j  LGD j
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Methodology: pricing model
U ( M )  1  C j   1  id   C j  1  re   cop j
U (M)
Cj
overall cash flows out
equity funding (%)
id
interest rate paid on interbank funding
re
gross return to shareholders
cop j
operative costs related to the loan
22