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

2 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 Lower loan overall credit risk Lower level of own funds

3 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.

4 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.

5 Methodology: pricing function Expected loss component Unexpected loss component Organizational component

6 Methodology: Modelling the impact of collaterals LGD C

7 Methodology: Modelling the impact of guarantees PD C

8 Methodology: pricing model \ cumulative distribution function for a standard normal random variable G (x) N (x) inverse cumulative distribution function for a standard normal random variable correlation proxy maturity adjustment effective maturity

9 Methodology: pricing model (1)  **** * ** ** jj j jj dej jj djj LGDPD cop LGDPD irC LGDPD iLGDPD Spread         (2)  GDJ PD  1 * 0  (3)         E MVCE MAXLGD J %45;0 * % 0 *  LGD 0  MVC (4)   06,15,215,11999, * 5,0 5,0 * *                             bMbLGDPDG R R GRNLGDC j

10 Methodology: limits 1) The analysis is based on a “technical” spread 2) C* is the “minimum capital required”

11 Methodology: comparative-static analysis 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:

12 Main results (01)

13 Main results (02) Elasticities of credit spread with respect to PD and LGD Pd  spread, LGD  spread, PD

14 Main results (03) Elasticities of capital requirement with respect to LGD and PD  C, LGD  C, PD PDd

15 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% ) alpha, mvc  spread,   spread, MVC

16 Main results (04) alpha, mvc  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% )

17 Main conclusions 1. Collaterals are the strongest mitigation tool 1.1. more evident when borrower’s PD is high No neutral regulation 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

18 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

19 Thanks, Riccardo De Lisa; Massimo Marchesi; Francesco Vallascas; Stefano Zedda;

20 Methodology: pricing model 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

21 Methodology: pricing model Posing E(M) = U(M) we have:

22 Methodology: pricing model overall cash flows out equity funding (%) interest rate paid on interbank funding gross return to shareholders operative costs related to the loan CjCj U (M)