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Description of Credit Risk Valuation 2/e |
This book offers an advanced introduction to the models of credit risk valuation. It concentrates on firm-value and reduced-form approaches and their applications in practice. Additionally, the book includes new models for valuing derivative securities with credit risk, focussing on options and forward contracts subject to counterparty default risk, but also treating options on credit-risky bonds and credit derivatives.
The text provides detailed descriptions of the state-of-the-art martingale methods and advanced numerical implementations based on multi-variate trees used to price derivative credit risk. Numerical examples illustrate the effects of credit risk on the prices of financial derivatives.
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Contents of Credit Risk Valuation 2/e |
1. Introduction
1.1 Motivation
1.1.1 Counterparty Default Risk
1.1.2 Derivatives on Defaultable Assets
1.1.3 Credit Derivatives
1.2 Objectives
1.3 Structure
2. Contingent Claim Valuation
2.1 Valuation in Discrete Time
2.1.1 Definitions
2.1.2 The Finite Setting
2.1.3 Extensions
2.2 Valuation in Continuous Time
2.2.1 Definitions
2.2.2 Arbitrage Pricing
2.2.3 Fundamental Asset Pricing Theorem
2.3 Applications in Continuous Time
2.3.1 Black-Scholes Model
2.3.2 Margrabe's Model
2.3.3 Heath-Jarrow-Morton Framework
2.3.4 Forward Measure
2.4 Applications in Discrete Time
2.4.1 Geometric Brownian Motion
2.4.2 Heath-Jarrow-Morton Forward Rates
2.5 Summary
3. Credit Risk Models
3.1 Pricing Credit-Risky Bonds
3.1.1 Traditional Methods
3.1.2 Firm Value Models
3.1.2.1 Merton's Model
3.1.2.2 Extensions and Applications of Merton's Model
3.1.2.3 Bankruptcy Costs and Endogenous Default
3.1.3 First Passage Time Models
3.1.4 Intensity Models
3.1.4.1 Jarrow-Turnbull Model
3.1.4.2 Jarrow-Lando-Turnbull Model
3.1.4.3 Other Intensity Models
3.2 Pricing Derivatives with Counterparty Risk
3.2.1 Firm Value Models
3.2.2 Intensity Models
3.2.3 Swaps
3.3 Pricing Credit Derivatives
3.3.1 Debt Insurance
3.3.2 Spread Derivatives
3.4 Empirical Evidence
3.5 Summary
4. A Firm Value Pricing Model for Derivatives with Counter-party Default Risk
4.1 The Credit Risk Model
4.2 Deterministic Liabilities
4.2.1 Prices for Vulnerable Options
4.2.2 Special Cases
4.2.2.1 Fixed Recovery Rate
4.2.2.2 Deterministic Claims
4.3 Stochastic Liabilities
4.3.1 Prices of Vulnerable Options
4.3.2 Special Cases
4.3.2.1 Asset Claims
4.3.2.2 Debt Claims
4.4 Gaussian Interest Rates and Deterministic Liabilities
4.4.1 Forward Measure
4.4.2 Prices of Vulnerable Stock Options
4.4.3 Prices of Vulnerable Bond Options
4.4.4 Special Cases
4.5 Gaussian Interest Rates and Stochastic Liabilities
4.5.1 Prices of Vulnerable Stock Options
4.5.2 Prices of Vulnerable Bond Options
4.5.3 Special Cases
4.6 Vulnerable Forward Contracts
4.7 Numerical Examples
4.7.1 Deterministic Interest Rates
4.7.2 Stochastic Interest Rates
4.7.3 Forward Contracts
4.8 Summary
4.9 Proofs of Propositions
4.9.1 Proof of Proposition 4.2.1
4.9.2 Proof of Proposition 4.3.1
4.9.3 Proof of Proposition 4.4.1
4.9.4 Proof of Proposition 4.5.1
5. A Hybrid Pricing Model for Contingent Claims with Credit Risk
5.1 The General Credit Risk Framework
5.1.1 Independence and Constant Parameters
5.1.2 Price Reduction and Bond Prices
5.1.3 Model Specifications
5.1.3.1 Arrival Rate of Default
5.1.3.2 Recovery Rate
5.1.3.3 Bankruptcy Costs
5.2 Implementations
5.2.1 Lattice with Deterministic Interest Rates
5.2.2 The Bankruptcy Process
5.2.3 An Extended Lattice Model
5.2.3.1 Stochastic Interest Rates
5.2.3.2 Recombining Lattice versus Binary Tree
5.3 Prices of Vulnerable Options
5.4 Recovering Observed Term Structures
5.4.1 Recovering the Risk-Free Term Structure
5.4.2 Recovering the Defaultable Term Structure
5.5 Default-Free Options on Risky Bonds
5.5.1 Put-Call Parity
5.6 Numerical Examples
5.6.1 Deterministic Interest Rates
5.6.2 Stochastic Interest Rates
5.7 Computational Cost
5.8 Summary
6. Pricing Credit Derivatives
6.1 Credit Derivative Instruments
6.1.1 Credit Derivatives of the First Type
6.1.2 Credit Derivatives of the Second Type
6.1.3 Other Credit Derivatives
6.2 Valuation of Credit Derivatives
6.2.1 Payoff Functions
6.2.1.1 Credit Forward Contracts
6.2.1.2 Credit Spread Options
6.3 The Compound Pricing Approach
6.3.1 Firm Value Model
6.3.2 Stochastic Interest Rates
6.3.3 Intensity and Hybrid Credit Risk Models
6.4 Numerical Examples
6.4.1 Deterministic Interest Rates
6.4.2 Stochastic Interest Rates
6.5 Pricing Spread Derivatives with a Reduced-Form Model
6.6 Credit Derivatives as Exchange Options
6.6.1 Process Specifications
6.6.2 Price of an Exchange Option
6.7 Credit Derivatives with Counterparty Default Risk
6.7.1 Price of an Exchange Option with Counterparty Default Risk
6.8 Summary
7. Conclusion
7.1 Summary
7.2 Practical Implications
7.3 Future Research
A. Useful Tools from Martingale Theory
A.1 Probabilistic Foundations
A.2 Process Classes
A.3 Martingales
A.4 Brownian Motion
A.5 Stochastic Integration
A.6 Change of Measure
References
List of Figures
List of Tables
Index
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