Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition, Santiago Moreno-Bromberg and Jean-Charles Rochet analyze corporate decisions such as dividend distribution, the issuance of securities, and capital structure and default. They pay particular attention to financial intermediaries, including banks and insurance companies.
The authors begin by recalling the ways that option-pricing techniques can be employed for the pricing of corporate debt and equity. They then present the dynamic model of the trade-off between taxes and bankruptcy costs and derive implications for optimal capital structure. The core chapter introduces the workhorse liquidity-management model'where liquidity and risk management decisions are made in order to minimize the costs of external finance. This model is used to study corporate finance decisions and specific features of banks and insurance companies. The book concludes by presenting the dynamic agency model, where financial frictions stem from the lack of interest alignment between a firm's manager and its financiers. The appendix contains an overview of the main mathematical tools used throughout the book.
Requiring some familiarity with stochastic calculus methods, Continuous-Time Models in Corporate Finance will be useful for students, researchers, and professionals who want to develop dynamic models of firms' financial decisions.
Santiago Moreno-Bromberg is senior researcher in the Center for Finance and Insurance at the University of Zurich. Jean-Charles Rochet is professor of banking at the University of Zurich, senior chair and head of research at the Swiss Finance Institute, and research director at the Toulouse School of Economics.
Preface xi
Introduction 1
1 Why Is Option Pricing Useful in Corporate Finance? 7
1.1 Modeling assumptions 7
1.2 Pricing corporate debt 9
1.3 Endogenous default date 11
1.3.1 The general form of the valuation equation 11
1.3.2 The price of a consol bond 13
1.4 Dynamic trade-off theory 15
1.4.1 Taxes and liquidation costs 16
1.4.2 Asset pricing 16
1.4.3 Financial decisions 19
1.4.4 Testable predictions 21 1.5 Further reading 22
2 The Base Liquidity-Management Model 26
2.1 The dynamics of net earnings 26
2.2 Risk-averse shareholders 27
2.2.1 Shareholder value 28
2.2.2 The optimal dividend flow 30
2.2.3 The value function 31
2.3 Risk-neutral shareholders 33
2.3.1 The dynamics of liquid reserves and the value function 34
2.3.2 The optimal dividend-distribution strategy 38
2.3.3 Economic implications 41
2.4 Further reading 42
3 Equity Issuance 45
3.1 Fixed issuance cost and stock-price dynamics 45
3.1.1 Optimal equity issuance with a fixed issuance cost 46
3.1.2 The impact of equity-issuance on the value function 48
3.1.3 When is equity issuance too costly? 50
3.1.4 Stock-price dynamics 51
3.2 Proportional issuance cost 53
3.2.1 The value function with a proportional issuance cost 54
3.2.2 Characterizing the optimal dividend-distribution barrier 54
3.2.3 The optimal equity-issuance strategy when the issuance cost is proportional 56
3.3 Uncertain refinancing opportunities 57
3.3.1 The cash-reserves dynamics with uncertain refinancing 57
3.3.2 The amount of uncertain refnancing 58
3.3.3 The refinancing region and the target cash level 60
3.4 Further reading 61
4 Applications to Banking 63
4.1 A simple continuous-time model of a bank 63
4.1.1 The model 63
4.1.2 The impact of a minimum-capital requirement 64
4.1.3 A minimum-capital requirement with recapitalization 66
4.2 A bank's portfolio problem 67
4.2.1 Setting up the stochastic-control problem 68
4.2.2 The value function and the first-best 69
4.3 Optimal bank funding 74
4.3.1 The model 74
4.3.2 The optimal funding strategies 77
4.3.3 Numerical analysis 80
4.4 Further reading 81
5 Applications to Insurance 84
5.1 The base liquidity-management model with large losses 84
5.1.1 The variational inequality in the presence of large losses 85
5.1.2 The value function 85
5.1.3 Computing the value function 88
5.2 Reinsuring Brownian risks 89
5.2.1 The dynamics of liquid reserves and the variational inequality 90
5.2.2 The partial-exposure region 91
5.2.3 The full-exposure region 93
5.2.4 Sensitivity analysis 94
5.3 Reinsuring large losses 96
5.3.1 The cash-reserves dynamics 96
5.3.2 The optimal reinsurance strategy 97
5.4 Further reading 98
6 Applications to Investment 101
6.1 The \q-model" of corporate investment 101
6.1.1 The stock of capital and its productivity 102
6.1.2 Shareholder value 103
6.1.3 Tobin's q 103
6.2 Introducing external financial frictions 105
6.2.1 The impact of liquidity constraints on firm value 106
6.2.2 The size-adjusted value function 107
6.2.3 Optimal investment and Tobin's q 109
6.3 Adopting a new technology 110
6.3.1 The model 110
6.3.2 The interaction between investment and dividend payouts 111
6.3.3 The optimal investment time 113
6.4 Further reading 115
7 Agency Frictions 117
7.1 Asset substitution and capital structure 117
7.1.1 The model 118
7.1.2 The risk-shifting problem 119
7.1.3 The impact of risk shifting on firm value 120
7.2 Dynamic capital structure 121
7.2.1 The model 121
7.2.2 The manager's continuation utility 123
7.2.3
