About the authors ANTONIO CASTAGNA is currently partner and co-founder of the consulting company Iason Ltd, focusing on the design of models to price complex derivatives and to measure financial, liquidity and credit risks. Previously he was with Banca IMI Milan, from 1999 to 2006, where he first worked as a market maker of cap/floors and swaptions and then set up the FX options market-making desk. He started his carrier in 1997 at IMI Bank Luxembourg, in the Risk Control Department. He graduated in Finance at LUISS University in Rome in 1995. He has written papers on different issues, including credit derivatives, managing exotic options risks and volatility smiles, and is also the author of FX Options and Smile Risk, John Wiley & Sons. FRANCESCO FEDE is a graduate of the LUISS University of Rome. From 1996 he worked for IMI Bank Lux as financial controller and risk manager. In 1998 he moved to Banca IMI Milan, where he started his career as a short-term interest derivative trader in 2001. Since then, he has covered many tasks in Treasury and ALM activities. Currently he is head of the Market Treasury desk of Banca IMI. Over the last couple of years he has focused on the pricing of liquidity risk for structured loans and derivative products, as well as the impact of liquidity risk on both trading and banking books.

• Preface xiiiAbout the authors xviiAbbreviations and acronyms xixPart I Liquidity and Banking Activity 11 Banks as lemons? 31.1 Introduction 31.2 The first wave 41.3 Banks as lemons? 71.4 The response 91.5 The second wave 131.6 Conclusion 152 A journey into liquidity 172.1 Introduction 172.2 Central bank liquidity 182.3 Funding liquidity 192.4 Market liquidity 222.5 The virtuous circle 242.6 The vicious circle 242.8 The role of the central bank, supervision and regulation 282.9 Conclusions 313 Too big to fail 333.1 Introduction 333.2 When giants fall 343.3 A hard lesson 363.4 Closer supervision 373.5 G-SIFI regulations 393.6 The next steps 413.7 Conclusion 444 The new framework 474.1 Introduction 474.2 Some basic liquidity risk measures 484.3 The first mover 504.4 Basel III: The new framework for liquidity risk measurement and monitoring 534.4.1 The liquidity coverage ratio 554.5 Inside the liquidity coverage ratio 634.6 The other metrics 664.7 Intraday liquidity risk 694.8 Beyond the ratios 724.9 Conclusion 745 Know thyself ! 755.1 Introduction 755.2 Some changes on the liabilities side 755.3 The role of leverage 795.4 The originate-to-distribute business model 825.5 The liquidity framework 845.6 Stress-testing and contingency funding plan 895.7 The CEBS identity card 955.8 Conclusions 975.9 Appendix: The CEBS Identity Card Annex (CEBS) 98Part II Tools To Manage Liquidity Risk 1096 Monitoring liquidity 1116.1 A taxonomy of cash flows 1116.2 Liquidity options 1146.3 Liquidity risk 1156.4 Quantitative liquidity risk measures 1186.4.1 The term structure of expected cash flows and the term structure of expected cumulated cash flows 1196.4.2 Liquidity generation capacity 1236.4.3 The term structure of available assets 1276.5 The term structure of expected liquidity 1346.6 Cash flows at risk and the term structure of liquidity at risk 1357 Liquidity buffer and term structure of funding 1437.1 Introduction 1437.2 Liquidity buffer and counterbalancing capacity 1437.3 The first cause of the need for a liquidity buffer: Maturity mismatch 1457.3.1 Some or all stressed scenarios do not occur 1497.3.2 The cost of the liquidity buffer for maturity mismatch 1527.3.3 Liquidity buffer costs when stressed scenarios do not occur 1587.3.4 A more general formula for liquidity buffer costs 1637.4 Funding assets with several liabilities 1687.5 Actual scenarios severer than predicted 1697.6 The term structure of available funding and the liquidity buffer 1717.6.1 The term structure of forward cumulated funding and how to use it 1757.7 Non-maturing liabilities 1797.7.1 Pricing of NML and cost of the liquidity buffer 1827.8 The second cause of the liquidity buffer: Collateral margining 1867.8.1 A method to set the liquidity buffer for derivative collateral 1867.8.2 The cost of the liquidity buffer for derivative collateral 1887.9 The third cause of the liquidity buffer: Off-balance-sheet commitments 1927.10 Basel III regulation and liquidity buffer 1948 Models for market risk factors 1998.1 Introduction 1998.2 Stock prices and FX rates 1998.3 Interest rate models 2018.3.1 One-factor models for the zero rate 2018.3.2 Vasicek model 2028.3.3 The CIR model 2028.3.4 The CIR++ model 2098.3.5 The basic affine jump diffusion model 2118.3.6 Numerical implementations 2128.3.7 Discrete version of the CIR model 2128.3.8 Monte Carlo methods 2148.3.9 Libor market model 2158.4 Default probabilities and credit spreads 2198.4.1 Structural models 2198.4.2 Reduced models 2218.4.3 Credit spreads 2238.5 Expected and minimum liquidity generation capacity of available bonds 2248.5.1 Value of the position in a defaultable coupon bond 2258.5.2 Expected value of the position in a coupon bond 2268.5.3 Haircut modelling 2278.5.4 Future value of a bond portfolio 2288.5.5 Calculating the quantile: a ∆ - Γ approximation of the portfolio 2288.5.6 Estimation of the CIR++ model for interest rates 2318.5.7 Estimation of the CIR++ model for default intensities 2338.5.8 Future liquidity from a single bond 2398.5.9 Future liquidity from more bonds 2408.6 Fair haircut for repo transactions and collateralized loans 2478.7 Adjustments to the value of illiquid bonds 2568.7.1 Liquid equivalent adjustment 2588.7.2 Price volatility adjustment 2618.A Expectation value of the bond with selling probability and spread 2709 Behavioural models 2779.1 Introduction 2779.2 Prepayment modelling 2779.2.1 Common approaches to modelling prepayments 2779.2.2 Hedging with an empirical model 2789.2.3 Effective hedging strategies of prepayment risk 2859.2.4 Conclusions on prepayment models 2889.2.5 Modelling prepayment decisions 2889.2.6 Modelling the losses upon prepayment 2909.2.7 Analytical approximation for ELoP1 2969.2.8 Valuing the ELoP using a VaR approach 2999.2.9 Extension to double rational prepayment 3039.2.10 Total prepayment cost 3059.2.11 Expected cash flows 3069.2.12 Mortgage pricing including prepayment costs 3089.3 Sight deposit and non-maturing liability modelling 3169.3.1 Modelling approaches 3179.3.2 The stochastic factor approach 3199.3.3 Economic evaluation and risk management of deposits 3249.3.4 Inclusion of bank runs 3349.4 Credit line modelling 3379.4.1 Measures to monitor usage of credit lines 3399.4.2 Modelling withdrawal intensity 3409.4.3 Liquidity management of credit lines 3419.4.4 Pricing of credit lines 3609.4.5 Commitment fee 3629.4.6 Adding the probability of default 3649.4.7 Spread option 3659.4.8 Incremental pricing 3689.A General decomposition of hedging swaps 3719.B Accuracy of mortgage rate approximation 3739.B.1 Internal model simulation engine 3739.B.2 Results 3749.C Accuracy of the approximated formula for correlated mortgage rate and prepayment intensity 3799.D Characteristic function of the integral 382Part III Pricing Liquidity Risk 38310 The links between credit risk and funding cost 38510.1 Introduction 38510.2 The axiom 38510.3 Cash flow fair values and discounting 38610.4 Critique of debit value adjustment 38910.4.1 Single-period case 38910.4.2 Multi-period case 39110.4.3 DVA as a funding benefit 39410.5 DVA for derivative contracts 39710.6 Extension to positive recovery and liquidity risk 40210.7 Dynamic replication of DVA 40410.7.1 The gain process 40410.7.2 Dynamic replication of a defaultable claim 40510.7.3 Objections to the statement ‘‘no long position in a bank’s own bonds is possible’’ 40910.7.4 DVA replication by the funding benefit 41010.7.5 DVA replication and bank’s franchise 41510.8 Recapitulation of results 41910.9 Accounting standard and DVA 41910.10 Distinction between price and value 42111 Cost of liquidity and fund transfer pricing 42511.1 Introduction 42511.2 Principles of transfer pricing 42511.2.1 Balance sheet 42511.2.2 Bank’s profits and losses 42611.3 Funding and banking activity 43111.4 Building a funding curve 43211.5 Including the funding cost in loan pricing 44611.5.1 Pricing of a fixed rate bullet loan 45011.6 Monitoring funding costs and risk control of refunding risk 45211.7 Funding costs and asset/liability management 45611.8 Internal fund transfer pricing system 45711.8.1 Multiple curves 45911.8.2 Single curve 46111.8.3 Implementation of funding policies 46511.9 Best practices and regulation 46812 Liquidity risk and the cost of funding in derivative contracts 47312.1 Pricing of derivative contracts under collateral agreements 47312.1.1 Pricing in a simple discrete setting 47512.1.2 The replicating portfolio in continuous time 48012.1.3 Pricing with a funding rate different from the investment rate 48312.1.4 Funding rate different from investment rate and repo rate 48912.1.5 Interest rate derivatives 49112.2 Pricing of collateralized derivative contracts when more than one currency is involved 49912.2.1 Contracts collateralized in a currency other than the payoff currency 49912.2.2 FX derivatives 50512.2.3 Interest rate derivatives 51112.2.4 Cross-currency swaps 51412.3 Valuation of non-collateralized interest rate swaps including funding costs 51812.3.1 The basic setup 51812.3.2 Hedging swap exposures and cash flows 51912.3.3 Funding spread modelling 52112.3.4 Strategy 1: Funding all cash flows at inception 52212.3.5 Strategy 2: Funding negative cash flows when they occur 52412.3.6 Including counterparty credit risk 52812.3.7 Practical examples 53113 A sort of conclusion: towards a new treasury? 53913.1 Introduction 53913.2 Organization of the treasury and the dealing room 53913.3 Banking vs trading book 54213.3.1 Collateralization 54213.3.2 Links amongst risks 54313.3.3 Production costs 545References 547Index 553

About the authors ANTONIO CASTAGNA is currently partner and co-founder of the consulting company Iason Ltd, focusing on the design of models to price complex derivatives and to measure financial, liquidity and credit risks. Previously he was with Banca IMI Milan, from 1999 to 2006, where he first worked as a market maker of cap/floors and swaptions and then set up the FX options market-making desk. He started his carrier in 1997 at IMI Bank Luxembourg, in the Risk Control Department. He graduated in Finance at LUISS University in Rome in 1995. He has written papers on different issues, including credit derivatives, managing exotic options risks and volatility smiles, and is also the author of FX Options and Smile Risk, John Wiley & Sons. FRANCESCO FEDE is a graduate of the LUISS University of Rome. From 1996 he worked for IMI Bank Lux as financial controller and risk manager. In 1998 he moved to Banca IMI Milan, where he started his career as a short-term interest derivative trader in 2001. Since then, he has covered many tasks in Treasury and ALM activities. Currently he is head of the Market Treasury desk of Banca IMI. Over the last couple of years he has focused on the pricing of liquidity risk for structured loans and derivative products, as well as the impact of liquidity risk on both trading and banking books.

• Preface xiiiAbout the authors xviiAbbreviations and acronyms xixPart I Liquidity and Banking Activity 11 Banks as lemons? 31.1 Introduction 31.2 The first wave 41.3 Banks as lemons? 71.4 The response 91.5 The second wave 131.6 Conclusion 152 A journey into liquidity 172.1 Introduction 172.2 Central bank liquidity 182.3 Funding liquidity 192.4 Market liquidity 222.5 The virtuous circle 242.6 The vicious circle 242.8 The role of the central bank, supervision and regulation 282.9 Conclusions 313 Too big to fail 333.1 Introduction 333.2 When giants fall 343.3 A hard lesson 363.4 Closer supervision 373.5 G-SIFI regulations 393.6 The next steps 413.7 Conclusion 444 The new framework 474.1 Introduction 474.2 Some basic liquidity risk measures 484.3 The first mover 504.4 Basel III: The new framework for liquidity risk measurement and monitoring 534.4.1 The liquidity coverage ratio 554.5 Inside the liquidity coverage ratio 634.6 The other metrics 664.7 Intraday liquidity risk 694.8 Beyond the ratios 724.9 Conclusion 745 Know thyself ! 755.1 Introduction 755.2 Some changes on the liabilities side 755.3 The role of leverage 795.4 The originate-to-distribute business model 825.5 The liquidity framework 845.6 Stress-testing and contingency funding plan 895.7 The CEBS identity card 955.8 Conclusions 975.9 Appendix: The CEBS Identity Card Annex (CEBS) 98Part II Tools To Manage Liquidity Risk 1096 Monitoring liquidity 1116.1 A taxonomy of cash flows 1116.2 Liquidity options 1146.3 Liquidity risk 1156.4 Quantitative liquidity risk measures 1186.4.1 The term structure of expected cash flows and the term structure of expected cumulated cash flows 1196.4.2 Liquidity generation capacity 1236.4.3 The term structure of available assets 1276.5 The term structure of expected liquidity 1346.6 Cash flows at risk and the term structure of liquidity at risk 1357 Liquidity buffer and term structure of funding 1437.1 Introduction 1437.2 Liquidity buffer and counterbalancing capacity 1437.3 The first cause of the need for a liquidity buffer: Maturity mismatch 1457.3.1 Some or all stressed scenarios do not occur 1497.3.2 The cost of the liquidity buffer for maturity mismatch 1527.3.3 Liquidity buffer costs when stressed scenarios do not occur 1587.3.4 A more general formula for liquidity buffer costs 1637.4 Funding assets with several liabilities 1687.5 Actual scenarios severer than predicted 1697.6 The term structure of available funding and the liquidity buffer 1717.6.1 The term structure of forward cumulated funding and how to use it 1757.7 Non-maturing liabilities 1797.7.1 Pricing of NML and cost of the liquidity buffer 1827.8 The second cause of the liquidity buffer: Collateral margining 1867.8.1 A method to set the liquidity buffer for derivative collateral 1867.8.2 The cost of the liquidity buffer for derivative collateral 1887.9 The third cause of the liquidity buffer: Off-balance-sheet commitments 1927.10 Basel III regulation and liquidity buffer 1948 Models for market risk factors 1998.1 Introduction 1998.2 Stock prices and FX rates 1998.3 Interest rate models 2018.3.1 One-factor models for the zero rate 2018.3.2 Vasicek model 2028.3.3 The CIR model 2028.3.4 The CIR++ model 2098.3.5 The basic affine jump diffusion model 2118.3.6 Numerical implementations 2128.3.7 Discrete version of the CIR model 2128.3.8 Monte Carlo methods 2148.3.9 Libor market model 2158.4 Default probabilities and credit spreads 2198.4.1 Structural models 2198.4.2 Reduced models 2218.4.3 Credit spreads 2238.5 Expected and minimum liquidity generation capacity of available bonds 2248.5.1 Value of the position in a defaultable coupon bond 2258.5.2 Expected value of the position in a coupon bond 2268.5.3 Haircut modelling 2278.5.4 Future value of a bond portfolio 2288.5.5 Calculating the quantile: a ∆ - Γ approximation of the portfolio 2288.5.6 Estimation of the CIR++ model for interest rates 2318.5.7 Estimation of the CIR++ model for default intensities 2338.5.8 Future liquidity from a single bond 2398.5.9 Future liquidity from more bonds 2408.6 Fair haircut for repo transactions and collateralized loans 2478.7 Adjustments to the value of illiquid bonds 2568.7.1 Liquid equivalent adjustment 2588.7.2 Price volatility adjustment 2618.A Expectation value of the bond with selling probability and spread 2709 Behavioural models 2779.1 Introduction 2779.2 Prepayment modelling 2779.2.1 Common approaches to modelling prepayments 2779.2.2 Hedging with an empirical model 2789.2.3 Effective hedging strategies of prepayment risk 2859.2.4 Conclusions on prepayment models 2889.2.5 Modelling prepayment decisions 2889.2.6 Modelling the losses upon prepayment 2909.2.7 Analytical approximation for ELoP1 2969.2.8 Valuing the ELoP using a VaR approach 2999.2.9 Extension to double rational prepayment 3039.2.10 Total prepayment cost 3059.2.11 Expected cash flows 3069.2.12 Mortgage pricing including prepayment costs 3089.3 Sight deposit and non-maturing liability modelling 3169.3.1 Modelling approaches 3179.3.2 The stochastic factor approach 3199.3.3 Economic evaluation and risk management of deposits 3249.3.4 Inclusion of bank runs 3349.4 Credit line modelling 3379.4.1 Measures to monitor usage of credit lines 3399.4.2 Modelling withdrawal intensity 3409.4.3 Liquidity management of credit lines 3419.4.4 Pricing of credit lines 3609.4.5 Commitment fee 3629.4.6 Adding the probability of default 3649.4.7 Spread option 3659.4.8 Incremental pricing 3689.A General decomposition of hedging swaps 3719.B Accuracy of mortgage rate approximation 3739.B.1 Internal model simulation engine 3739.B.2 Results 3749.C Accuracy of the approximated formula for correlated mortgage rate and prepayment intensity 3799.D Characteristic function of the integral 382Part III Pricing Liquidity Risk 38310 The links between credit risk and funding cost 38510.1 Introduction 38510.2 The axiom 38510.3 Cash flow fair values and discounting 38610.4 Critique of debit value adjustment 38910.4.1 Single-period case 38910.4.2 Multi-period case 39110.4.3 DVA as a funding benefit 39410.5 DVA for derivative contracts 39710.6 Extension to positive recovery and liquidity risk 40210.7 Dynamic replication of DVA 40410.7.1 The gain process 40410.7.2 Dynamic replication of a defaultable claim 40510.7.3 Objections to the statement ‘‘no long position in a bank’s own bonds is possible’’ 40910.7.4 DVA replication by the funding benefit 41010.7.5 DVA replication and bank’s franchise 41510.8 Recapitulation of results 41910.9 Accounting standard and DVA 41910.10 Distinction between price and value 42111 Cost of liquidity and fund transfer pricing 42511.1 Introduction 42511.2 Principles of transfer pricing 42511.2.1 Balance sheet 42511.2.2 Bank’s profits and losses 42611.3 Funding and banking activity 43111.4 Building a funding curve 43211.5 Including the funding cost in loan pricing 44611.5.1 Pricing of a fixed rate bullet loan 45011.6 Monitoring funding costs and risk control of refunding risk 45211.7 Funding costs and asset/liability management 45611.8 Internal fund transfer pricing system 45711.8.1 Multiple curves 45911.8.2 Single curve 46111.8.3 Implementation of funding policies 46511.9 Best practices and regulation 46812 Liquidity risk and the cost of funding in derivative contracts 47312.1 Pricing of derivative contracts under collateral agreements 47312.1.1 Pricing in a simple discrete setting 47512.1.2 The replicating portfolio in continuous time 48012.1.3 Pricing with a funding rate different from the investment rate 48312.1.4 Funding rate different from investment rate and repo rate 48912.1.5 Interest rate derivatives 49112.2 Pricing of collateralized derivative contracts when more than one currency is involved 49912.2.1 Contracts collateralized in a currency other than the payoff currency 49912.2.2 FX derivatives 50512.2.3 Interest rate derivatives 51112.2.4 Cross-currency swaps 51412.3 Valuation of non-collateralized interest rate swaps including funding costs 51812.3.1 The basic setup 51812.3.2 Hedging swap exposures and cash flows 51912.3.3 Funding spread modelling 52112.3.4 Strategy 1: Funding all cash flows at inception 52212.3.5 Strategy 2: Funding negative cash flows when they occur 52412.3.6 Including counterparty credit risk 52812.3.7 Practical examples 53113 A sort of conclusion: towards a new treasury? 53913.1 Introduction 53913.2 Organization of the treasury and the dealing room 53913.3 Banking vs trading book 54213.3.1 Collateralization 54213.3.2 Links amongst risks 54313.3.3 Production costs 545References 547Index 553

About the authors ANTONIO CASTAGNA is currently partner and co-founder of the consulting company Iason Ltd, focusing on the design of models to price complex derivatives and to measure financial, liquidity and credit risks. Previously he was with Banca IMI Milan, from 1999 to 2006, where he first worked as a market maker of cap/floors and swaptions and then set up the FX options market-making desk. He started his carrier in 1997 at IMI Bank Luxembourg, in the Risk Control Department. He graduated in Finance at LUISS University in Rome in 1995. He has written papers on different issues, including credit derivatives, managing exotic options risks and volatility smiles, and is also the author of FX Options and Smile Risk, John Wiley & Sons. FRANCESCO FEDE is a graduate of the LUISS University of Rome. From 1996 he worked for IMI Bank Lux as financial controller and risk manager. In 1998 he moved to Banca IMI Milan, where he started his career as a short-term interest derivative trader in 2001. Since then, he has covered many tasks in Treasury and ALM activities. Currently he is head of the Market Treasury desk of Banca IMI. Over the last couple of years he has focused on the pricing of liquidity risk for structured loans and derivative products, as well as the impact of liquidity risk on both trading and banking books.

• Preface xiiiAbout the authors xviiAbbreviations and acronyms xixPart I Liquidity and Banking Activity 11 Banks as lemons? 31.1 Introduction 31.2 The first wave 41.3 Banks as lemons? 71.4 The response 91.5 The second wave 131.6 Conclusion 152 A journey into liquidity 172.1 Introduction 172.2 Central bank liquidity 182.3 Funding liquidity 192.4 Market liquidity 222.5 The virtuous circle 242.6 The vicious circle 242.8 The role of the central bank, supervision and regulation 282.9 Conclusions 313 Too big to fail 333.1 Introduction 333.2 When giants fall 343.3 A hard lesson 363.4 Closer supervision 373.5 G-SIFI regulations 393.6 The next steps 413.7 Conclusion 444 The new framework 474.1 Introduction 474.2 Some basic liquidity risk measures 484.3 The first mover 504.4 Basel III: The new framework for liquidity risk measurement and monitoring 534.4.1 The liquidity coverage ratio 554.5 Inside the liquidity coverage ratio 634.6 The other metrics 664.7 Intraday liquidity risk 694.8 Beyond the ratios 724.9 Conclusion 745 Know thyself ! 755.1 Introduction 755.2 Some changes on the liabilities side 755.3 The role of leverage 795.4 The originate-to-distribute business model 825.5 The liquidity framework 845.6 Stress-testing and contingency funding plan 895.7 The CEBS identity card 955.8 Conclusions 975.9 Appendix: The CEBS Identity Card Annex (CEBS) 98Part II Tools To Manage Liquidity Risk 1096 Monitoring liquidity 1116.1 A taxonomy of cash flows 1116.2 Liquidity options 1146.3 Liquidity risk 1156.4 Quantitative liquidity risk measures 1186.4.1 The term structure of expected cash flows and the term structure of expected cumulated cash flows 1196.4.2 Liquidity generation capacity 1236.4.3 The term structure of available assets 1276.5 The term structure of expected liquidity 1346.6 Cash flows at risk and the term structure of liquidity at risk 1357 Liquidity buffer and term structure of funding 1437.1 Introduction 1437.2 Liquidity buffer and counterbalancing capacity 1437.3 The first cause of the need for a liquidity buffer: Maturity mismatch 1457.3.1 Some or all stressed scenarios do not occur 1497.3.2 The cost of the liquidity buffer for maturity mismatch 1527.3.3 Liquidity buffer costs when stressed scenarios do not occur 1587.3.4 A more general formula for liquidity buffer costs 1637.4 Funding assets with several liabilities 1687.5 Actual scenarios severer than predicted 1697.6 The term structure of available funding and the liquidity buffer 1717.6.1 The term structure of forward cumulated funding and how to use it 1757.7 Non-maturing liabilities 1797.7.1 Pricing of NML and cost of the liquidity buffer 1827.8 The second cause of the liquidity buffer: Collateral margining 1867.8.1 A method to set the liquidity buffer for derivative collateral 1867.8.2 The cost of the liquidity buffer for derivative collateral 1887.9 The third cause of the liquidity buffer: Off-balance-sheet commitments 1927.10 Basel III regulation and liquidity buffer 1948 Models for market risk factors 1998.1 Introduction 1998.2 Stock prices and FX rates 1998.3 Interest rate models 2018.3.1 One-factor models for the zero rate 2018.3.2 Vasicek model 2028.3.3 The CIR model 2028.3.4 The CIR++ model 2098.3.5 The basic affine jump diffusion model 2118.3.6 Numerical implementations 2128.3.7 Discrete version of the CIR model 2128.3.8 Monte Carlo methods 2148.3.9 Libor market model 2158.4 Default probabilities and credit spreads 2198.4.1 Structural models 2198.4.2 Reduced models 2218.4.3 Credit spreads 2238.5 Expected and minimum liquidity generation capacity of available bonds 2248.5.1 Value of the position in a defaultable coupon bond 2258.5.2 Expected value of the position in a coupon bond 2268.5.3 Haircut modelling 2278.5.4 Future value of a bond portfolio 2288.5.5 Calculating the quantile: a ∆ - Γ approximation of the portfolio 2288.5.6 Estimation of the CIR++ model for interest rates 2318.5.7 Estimation of the CIR++ model for default intensities 2338.5.8 Future liquidity from a single bond 2398.5.9 Future liquidity from more bonds 2408.6 Fair haircut for repo transactions and collateralized loans 2478.7 Adjustments to the value of illiquid bonds 2568.7.1 Liquid equivalent adjustment 2588.7.2 Price volatility adjustment 2618.A Expectation value of the bond with selling probability and spread 2709 Behavioural models 2779.1 Introduction 2779.2 Prepayment modelling 2779.2.1 Common approaches to modelling prepayments 2779.2.2 Hedging with an empirical model 2789.2.3 Effective hedging strategies of prepayment risk 2859.2.4 Conclusions on prepayment models 2889.2.5 Modelling prepayment decisions 2889.2.6 Modelling the losses upon prepayment 2909.2.7 Analytical approximation for ELoP1 2969.2.8 Valuing the ELoP using a VaR approach 2999.2.9 Extension to double rational prepayment 3039.2.10 Total prepayment cost 3059.2.11 Expected cash flows 3069.2.12 Mortgage pricing including prepayment costs 3089.3 Sight deposit and non-maturing liability modelling 3169.3.1 Modelling approaches 3179.3.2 The stochastic factor approach 3199.3.3 Economic evaluation and risk management of deposits 3249.3.4 Inclusion of bank runs 3349.4 Credit line modelling 3379.4.1 Measures to monitor usage of credit lines 3399.4.2 Modelling withdrawal intensity 3409.4.3 Liquidity management of credit lines 3419.4.4 Pricing of credit lines 3609.4.5 Commitment fee 3629.4.6 Adding the probability of default 3649.4.7 Spread option 3659.4.8 Incremental pricing 3689.A General decomposition of hedging swaps 3719.B Accuracy of mortgage rate approximation 3739.B.1 Internal model simulation engine 3739.B.2 Results 3749.C Accuracy of the approximated formula for correlated mortgage rate and prepayment intensity 3799.D Characteristic function of the integral 382Part III Pricing Liquidity Risk 38310 The links between credit risk and funding cost 38510.1 Introduction 38510.2 The axiom 38510.3 Cash flow fair values and discounting 38610.4 Critique of debit value adjustment 38910.4.1 Single-period case 38910.4.2 Multi-period case 39110.4.3 DVA as a funding benefit 39410.5 DVA for derivative contracts 39710.6 Extension to positive recovery and liquidity risk 40210.7 Dynamic replication of DVA 40410.7.1 The gain process 40410.7.2 Dynamic replication of a defaultable claim 40510.7.3 Objections to the statement ‘‘no long position in a bank’s own bonds is possible’’ 40910.7.4 DVA replication by the funding benefit 41010.7.5 DVA replication and bank’s franchise 41510.8 Recapitulation of results 41910.9 Accounting standard and DVA 41910.10 Distinction between price and value 42111 Cost of liquidity and fund transfer pricing 42511.1 Introduction 42511.2 Principles of transfer pricing 42511.2.1 Balance sheet 42511.2.2 Bank’s profits and losses 42611.3 Funding and banking activity 43111.4 Building a funding curve 43211.5 Including the funding cost in loan pricing 44611.5.1 Pricing of a fixed rate bullet loan 45011.6 Monitoring funding costs and risk control of refunding risk 45211.7 Funding costs and asset/liability management 45611.8 Internal fund transfer pricing system 45711.8.1 Multiple curves 45911.8.2 Single curve 46111.8.3 Implementation of funding policies 46511.9 Best practices and regulation 46812 Liquidity risk and the cost of funding in derivative contracts 47312.1 Pricing of derivative contracts under collateral agreements 47312.1.1 Pricing in a simple discrete setting 47512.1.2 The replicating portfolio in continuous time 48012.1.3 Pricing with a funding rate different from the investment rate 48312.1.4 Funding rate different from investment rate and repo rate 48912.1.5 Interest rate derivatives 49112.2 Pricing of collateralized derivative contracts when more than one currency is involved 49912.2.1 Contracts collateralized in a currency other than the payoff currency 49912.2.2 FX derivatives 50512.2.3 Interest rate derivatives 51112.2.4 Cross-currency swaps 51412.3 Valuation of non-collateralized interest rate swaps including funding costs 51812.3.1 The basic setup 51812.3.2 Hedging swap exposures and cash flows 51912.3.3 Funding spread modelling 52112.3.4 Strategy 1: Funding all cash flows at inception 52212.3.5 Strategy 2: Funding negative cash flows when they occur 52412.3.6 Including counterparty credit risk 52812.3.7 Practical examples 53113 A sort of conclusion: towards a new treasury? 53913.1 Introduction 53913.2 Organization of the treasury and the dealing room 53913.3 Banking vs trading book 54213.3.1 Collateralization 54213.3.2 Links amongst risks 54313.3.3 Production costs 545References 547Index 553