Contents
I Introduction to Finance and the Mathematics of Continuous-Time Models
1 Modern Finance
2 Introduction to Portfolio Selection and Capital Market Theory: Static Analysis
2.1 Introduction
2.2 One-Period Portfolio Selection
2.3 Risk Measures for Securities and Portfolios in the One-Period Model
2.4 Spanning, Separation, and Mutual-Fund Theorems
3 On the Mathematics and Economics Assumptions of Continuous-Time Models
3.1 Introduction
3.2 Continuous-Sample-Path Processes with “No Rare Events”
3.3 Continuous-Sample-Path Processes with “Rare Events”
3.4 Discontinuous-Sample-Path Processes with “Rare Events”
II Optimum Consumption and Portfolio Selection in Continuous-Time Models
4 Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case
4.1 Introduction
4.2 Dynamics of the Model: The Budget Equation
4.3 The Two-Asset Model
4.4 Constant Relative Risk Aversion
4.5 Dynamic Behavior and the Bequest Valuation Function
4.6 Infinite Time Horizon
4.7 Economic Interpretation of the Optimal Decision Rules for Portfolio Selection and Consumption
4.8 Extension to Many Assets
4.9 Constant Absolute Risk Aversion
4.10 Other Extensions of the Model
5 Optimum Consumption and Portfolio Rules in a Continuous-time Model
5.1 Introduction
5.2 A Digression on Itˆo Processes
5.3 Asset-Price Dynamics and the Budget Equation
5.4 Optimal Portfolio and Consumption Rules: The Equations of Optimality
5.5 Log-Normality of Prices and the Continuous-Time Analog to Tobin-Markowitz Mean-Variance Analysis
5.6 Explicit Solutions for a Particular Class of Utility Functions
5.7 Noncapital Gains Income: Wages
5.8 Poisson Processes
5.9 Alternative Price Expectations to the Geometric Brownian Motion
5.10 Conclusion
6 Further Developments in the Theory of Optimal Consumption and Portfolio Selection
6.1 Introduction
6.2 The Cox-Huang Alternative to Stochastic Dynamic Programming
6.2.1 The Growth-Optimum Portfolio Strategy
6.2.2 The Cox-Huang Solution of the Intertemporal Consumption-Investment Problem
6.2.3 The Relation Between the Cox-Huang and Dynamic Programming Solutions
6.3 Optimal Portfolio Rules when the Nonnegativity Constraint on Consumption is Binding
6.4 Generalized Preferences and Their Impact on Optimal Portfolio Demands
III Warrant and Option Pricing Theory
7 A Complete Model of Warrant Pricing that Maximizes Utility
7.1 Introduction
7.2 Cash-Stock Portfolio Analysis
7.3 Recapitulation of the 1965 Model
7.4 Determining Average Stock Yield
7.5 Determining Warrant Holdings and Prices
7.6 Digression: General Equilibrium Pricing
7.7 Utility-Maximizing Warrant Pricing: The Important “Incipient” Case
7.8 Explicit Solutions
7.9 Warrants Never to be Converted
7.10 Exact Solution to the Perpetual Warrant Case
7.11 Illustrative Example
7.12 Proof of the Superiority of Yield ofWarrants Over Yield of Common Stock
7.13 Conclusion
8 Theory of rational option pricing
8.1 Introduction
8.2 Restrictions on Rational Option Pricing
8.3 Effects of Dividends and Changing Exercise Price
8.4 Restrictions on Rational Put Option Pricing
8.5 Rational Option Pricing Along Black-Scholes Lines
8.6 An Alternative Derivation of the Black-Scholes Model
8.7 Extension of the Model to Include Dividend Payments And Exercise Price Changes
8.8 Valuing an American Put Option
8.9 Valuing the “Down-and-Out” Call Option
8.10 Valuing a Callable Warrant
8.11 Conclusion
9 Option Pricing When Underlying Stock Returns are Discontinuous
9.1 Introduction
9.2 The Stock Price and Option Price Dynamics
9.3 An Option Pricing Formula
9.4 A Possible Answer to an Empirical Puzzle
10 Further Developments in Option Pricing Theory
10.1 Introduction
10.2 Cox-Ross “Risk-Neutral” Pricing and the Binomial Option Pricing Model
10.3 Pricing Options on Futures Contracts
IV Contingent-Claims Analysis in the Theory of Corporate Finance and Financial Intermediation
11 A Dynamic General Equilibrium Model of the Asset Market and Its Application to the Pricing of the Capital Structure of the Firm
11.1 Introduction
11.2 A Partial-Equilibrium One-Period Model
11.3 Some Examples
11.4 A General Intertemporal Equilibrium Model of the Asset Market
11.5 Model I: A Constant Interest Rate Assumption
11.6 Model II: The “No Riskless Asset” Case
11.7 Model III: The General Model
11.8 Conclusion
12 On the Pricing of Corporate Debt: The Risk Structure of Interest Rates
12.1 Introduction
12.2 On The Pricing of Corporate Liabilities
12.3 On Pricing “Risky” Discount Bonds
12.4 A Comparative Statics Analysis of the Risk Structure
12.5 On the Modigliani-Miller Theorem with Bankruptcy
12.6 On the Pricing of Risky Coupon Bonds
12.7 Conclusion
13 On the Pricing of Contingent Claims and the Modigliani-Miller Theorem
13.1 Introduction
13.2 A general derivation of a contingent claim price
13.3 On the Modigliani-Miller Theorem with Bankruptcy
13.4 Applications of Contingent-Claims Analysis in Corporate Finance
14 Financial Intermediation in the Continuous-Time Model
14.1 Introduction
14.2 Derivative-Security Pricing with Transactions Costs
14.3 Production Theory for Zero-Transaction-Cost Financial Intermediaries
14.4 Risk Management for Financial Intermediaries
14.5 On the Role of Efficient Financial Intermediation in the Continuous-Time Model
14.6 Afterword: Policy and Strategy in Financial Intermediation
V An Intertemporal Equilibrium Theory of Finance
15 An Intertemporal Capital Asset Pricing Model
15.1 Introduction
15.2 Capital Market Structure
15.3 Asset Value and Rate of Return Dynamics
15.4 Preference Structure and Budget Equation Dynamics
15.5 The Equations of Optimality: The Demand Functions for Assets
15.6 Constant Investment Opportunity Set
15.7 Generalized Separation: A Three-Fund Theorem
15.8 The Equilibrium Yield Relationship among Assets
15.9 Empirical Evidence
15.10An (m + 2)-Fund Theorem and the Security Market Hyperplane
15.11The Consumption-Based Capital Asset Pricing Model
15.12Conclusion
16 A Complete-Markets General Equilibrium Theory of Finance in Continuous Time
16.1 Introduction
16.2 Financial Intermediation with Dynamically-Complete Markets
16.3 Optimal Consumption and Portfolio Rules with Dynamically-Complete Markets
16.4 General Equilibrium: The Case of Pure Exchange
16.5 General Equilibrium: The Case of Production
16.6 A General Equilibrium Model in which the Capital Asset Pricing Model Obtains
16.7 Conclusion
VI Applications of the Continuous-Time Model to Selected Issues in Public Finance: Long-Run Economic Growth, Public Pension Plans, Deposit Insurance, Loan Guarantees, and Endowment Management for Universities
17 An Asymptotic Theory of Growth Under Uncertainty
17.1 Introduction
17.2 The Model
17.3 The Steady-State Distribution for k
17.4 The Cobb-Douglas/Constant Savings Function Economy
17.5 The Stochastic Ramsey Problem
18 On Consumption-Indexed Public Pension Plans
18.1 Introduction
18.2 A Simple Intertemporal Equilibrium Model
18.3 On the Merits and Feasibility of a Consumption-Indexed Public Plan
19 An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance: An Application of Modern Option Pricing Theory
19.1 Introduction
19.2 A model for pricing deposit insurance
20 On the Cost of Deposit Insurance When There are Surveillance Costs
20.1 Introduction
20.2 Assumptions of the Model
20.3 The Evaluation of FDIC Liabilities
20.4 The Evaluation of Bank Equity
20.5 On the Equilibrium Deposit Rate
20.6 Conclusion
21 Optimal Investment Strategies for University Endowment Funds
21.1 Introduction
21.2 Overview of Basic Insights and Prescriptions for Policy
21.3 The Model
21.4 Optimal Endowment Management with Other Sources of Income | 