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*: University of Cagliari (Economics of Financial Intermediaries; Financial Mathematics)

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.

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*: University of Cagliari (Economics of Financial Intermediaries; Financial Mathematics)

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  1. Assessing the effects of collaterals and guarantee on loan pricing under the IRB approach: a comparative-static analysisR. 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: • risk-sensitive capital adequacy; • Fully recognition of “mitigation techniques” (as collaterals and guarantees – C&G) . 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 Organizational component Unexpected loss component

  6. Methodology: Modelling the impact of collaterals LGD C

  7. Methodology: Modelling the impact of guarantees PD C

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

  9. ( ) ( ) * * * ´ ´ + ´ - PD LGD 1 i C r i cop j j d j e d j = + + Spread * * * * * * - ´ - ´ - ´ 1 PD LGD 1 PD LGD 1 PD LGD j j j j j j ( ) * = - a ´ + a ´ PD 1 PD PD a ³ 0 J D G - é ù E MVC * * = ´ £  LGD MAX 0 ; 45 % 0 LGD 45 % ³ MVC 0 ê ú J E ë û é ù é ù 0 , 5 æ ö R [ ] ( ) ( ) ( ) ( ) ( ) - - ê ú * 0 , 5 1 * * ê ú = ´ - ´ + ´ - ´ ´ - ´ ´ + - ´ ´ ç ÷ C LGD N 1 R G PD G 0 , 999 PD LGD 1 1 , 5 b 1 M 2 , 5 b 1 , 06 j ê ú - ê ú 1 R è ø ë û ë û Methodology: pricing model (1) (2) (3) (4)

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

  11. 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

  12. 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 Main results (01)

  13. e spread, LGD e spread, PD 0.6 0.5 0.4 0.3 0.2 0.1 Pd 0.02 0.04 0.06 0.08 Main results (02) Elasticities of credit spread with respect to PD and LGD

  14. 1 0.9 e C, LGD 0.8 0.7 0.6 0.5 e C, PD 0.4 0.3 PDd 0.02 0.04 0.06 0.08 Main results (03) Elasticities of capital requirement with respect to LGD and PD

  15. alpha , mvc 0.2 0.4 0.6 0.8 1 -0.1 e spread, a -0.2 -0.3 e spread, MVC -0.4 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%)

  16. 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%) alpha , mvc 0.2 0.4 0.6 0.8 1 e spread, a -0.1 -0.2 -0.3 e spread, MVC -0.4

  17. 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

  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; delisa@unica.it Massimo Marchesi; massimo.marchesi@cec.eu.int Francesco Vallascas; francesco.vallascas@unica.it Stefano Zedda; szedda@unica.it

  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 U (M) overall cash flows out Cj equity funding (%) interest rate paid on interbank funding gross return to shareholders operative costs related to the loan

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