Black and Scholes (1973) and Merton (1973, 1974) (hereafter referred to as BSM) introduced the contingent claim approach (CCA) to the valuation of corporate debt and equity. The BSM modeling framework is also named the "structural" approach to risky debt valuation.
The CCA considers all stakeholders of the corporation as holding contingent claims on the assets of the corporation. Each claim holder has different priorities, maturities and conditions for payouts. It is based on the principle that all the assets belong to all the liability holders.
The BSM modeling framework gives the basic fundamental version of the structural model where default is assumed to occur when the net asset value of the firm at the maturity of the pure-discount debt becomes negative, i.e., market value of the assets of the firm falls below the face value of the firm's liabilities. In a regime of limited liability, the shareholders of the firm have the option to default on the firm's debt. Equity can be viewed as a European call option on the firm's assets with a strike price equal to the face value of the firm's debt. Actually, CCA can be used to value all the components of the firm's liabilities, equity, warrants, debt, contingent convertible debt, guarantees, etc.
In the four volumes we present the major academic research on CCA in corporate finance starting from 1973, with seminal papers of Black and Scholes (1973) and Merton (1973, 1974). Volume I covers the foundation of CCA and contributions on equity valuation. Volume II focuses on corporate debt valuation and the capital structure of the firm. Volume III presents empirical evidence on the valuation of debt instruments as well as applications of the CCA to various financial arrangements. The papers in Volume IV show how to apply the CCA to analyze sovereign credit risk, contingent convertible bonds (CoCos), deposit insurance and loan guarantees.
Volume 1: Foundations of CCA and Equity Valuation
Volume 1 presents the seminal papers of Black and Scholes (1973) and Merton (1973, 1974). This volume also includes papers that specifically price equity as a call option on the corporation. It introduces warrants, convertible bonds and taxation as contingent claims on the corporation. It highlights the strong relationship between the CCA and the Modigliani-Miller (M&M) Theorems, and the relation to the Capital Assets Pricing Model (CAPM).
Volume 2: Corporate Debt Valuation with CCA
Volume 2 concentrates on corporate bond valuation by introducing various types of bonds with different covenants as well as introducing various conditions that trigger default. While empirical evidence indicates that the simple Merton's model underestimates the credit spreads, additional risk factors like jumps can be used to resolve it.
Volume 3: Empirical Testing and Applications of CCA
Volume 3 includes papers that look at issues in corporate finance that can be explained with the CCA approach. These issues include the effect of dividend policy on the valuation of debt and equity, the pricing of employee stock options and many other issues of corporate governance.
Volume 4: Contingent Claims Approach for Banks and Sovereign Debt
Volume 4 focuses on the application of the contingent claim approach to banks and other financial intermediaries. Regulation of the banking industry led to the creation of new financial securities (e.g., CoCos) and new types of stakeholders (e.g., deposit insurers).
Debt and equity before the maturity |
|
Probability of default as a function of the volatility and the current distance from the debt |
|
|
Impact of a dividend on the probability of default |
|
Payoff of senior and junior debt at maturity |
|
|
Contents:
- Volume 1: Foundations of CCA and Equity Valuation:
- Foundations of CCA:
- The Pricing of Options and Corporate Liabilities (Fischer Black and Myron Scholes)
- Theory of Rational Option Pricing (Robert C Merton)
- On the Pricing of Corporate Debt: The Risk Structure of Interest Rates (Robert C Merton)
- Valuing Corporate Securities: Some Effects of Bond Indenture Provisions (Fischer Black and John C Cox)
- The Role of Contingent Claims Analysis in Corporate Finance (Scott P Mason and Robert C Merton)
- Credit Risk Revisited (Michel Crouhy, Dan Galai & Robert Mark)
- The Relation between the Risk-Neutral and Physical Probabilities of Default (Michel Crouhy and Dan Galai)
- Pricing of Equity and Warrants:
- The Option Pricing Model and the Risk Factor of Stock (Dan Galai and Ronald W Masulis)
- Pricing of Warrants and the Value of the Firm (Dan Galai and Meir I Schneller)
- Warrant Valuation and Exercise Strategy (David C Emanuel)
- Warrant Exercise and Bond Conversion in Competitive Markets (George M Constantinides)
- Warrant Exercise, Dividends and Reinvestment Policy (Chester S Spatt and Frederic P Sterbenz)
- The Interaction between the Financial and Investment Decisions of the Firm: The Case of Issuing Warrants in a Levered Firm (Michel Crouhy and Dan Galai)
- New Warrant Issues Valuation with Leverage and Equity Model Errors (Jean-Guy Simonato)
- Convertible Securities:
- A Contingent-Claims Valuation of Convertible Securities (Jonathan E Ingersoll, Jr)
- Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion (M J Brennan and E S Schwartz)
- Convertible Debt and Shareholder Incentives (Christian Dorion, Pascal François, Gunnar Grass and Alexandre Jeanneret)
- Volume 2: Corporate Debt Valuation with CCA:
- Framework:
- The Valuation of Corporate Liabilities as Compound Options (Robert Geske)
- Corporate Debt Value, Bond Covenants, and Optimal Capital Structure (Hayne E Leland)
- Optimal Capital Structure, Endogenous Bankruptcy and the Term Structure of Credit Spreads (Hayne E Leland and Klaus Bjerre Toft)
- Strategic Debt Service (Pierre Mella-Barral and William Perraudin)
- Modigliani–Miller and CCA:
- On the Pricing of Contingent Claims and the Modigliani–Miller Theorem (Robert C Merton)
- Taxes, M-M Propositions and Government's Implicit Cost of Capital in Investment Projects in the Private Sector (Dan Galai)
- Taxation and Accounting:
- Corporate Income Taxes, Valuation, and the Problem of Optimal Capital Structure (M J Brennan and E S Schwartz)
- Corporate Income Taxes and the Valuation of the Claims on the Corporation (Dan Galai)
- Option Pricing-Based Bond Value Estimates and a Fundamental Components Approach to Account for Corporate Debt (Mary E Barth, Wayne R Landsman and Richard J Rendleman, Jr)
- Stochastic Interest Rates:
- The Pricing of Risky Debt When Interest Rates are Stochastic (David C Shimko, Naohiko Tejima and Donald R van Deventer)
- A Simple Approach to Valuing Risky Fixed and Floating Rate Debt (Francis A Longstaff and Eduardo S Schwartz)
- Valuing Risky Fixed Rate Debt: An Extension (Eric Briys and François de Varenne)
- Term Structures of Credit Spreads with Incomplete Accounting Information (Darrell Duffie and David Lando)
- Liquidation Triggers:
- Valuing Corporate Liabilities When the Default Threshold is not an Absorbing Barrier (Franck Moraux)
- Capital Structure and Asset Prices: Some Effects of Bankruptcy Procedures (Pascal François and Erwan Morellec)
- Liquidation Triggers and the Valuation of Equity and Debt (Dan Galai, Alon Raviv and Zvi Wiener)
- Moody's KMV Model:
- Credit Valuation (Oldrich Alfons Vasicek)
- The Merton/KMV Approach to Pricing Credit Risk (Rangarajan K Sundaram)
- Quantifying Credit Risk I: Default Prediction (Stephen Kealhofer)
- Modeling Default Risk (Peter Crosbie and Jeffrey Bohn)
- Volume 3: Empirical Testing and Applications of CCA:
- Empirical Studies:
- Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation (E Philip Jones, Scott P Mason and Eric Rosenfeld)
- Determinants of the Ratings and Yields on Corporate Bonds: Tests of the Contingent Claims Model (Joseph P Ogden)
- An Empirical Investigation of US Firms in Reorganization (Julian R Franks and Walter N Torous)
- Some Empirical Estimates of the Risk Structure of Interest Rates (Oded Sarig and Arthur Warga)
- Costly Financing, Optimal Payout Policies and the Valuation of Corporate Debt (Viral Acharya, Jing-Zhi Huang, Marti Subrahmanyam and Rangarajan Sundaram)
- Testing Merton's Model for Credit Spreads on Zero-Coupon Bonds (Gordon Gemmill)
- Estimating Structural Bond Pricing Models (Jan Ericsson and Joel Reneby)
- Estimating Structural Models of Corporate Bond Prices (Max Bruche)
- Strategic Actions and Credit Spreads: An Empirical Investigation (Sergei A Davydenko and Ilya A Strebulaev)
- Credit Calibration with Structural Models and Equity Return Swap Valuation under Counterparty Risk (Damiano Brigo, Massimo Morini and Marco Tarenghi)
- Can Structural Models Price Default Risk? Evidence from Bond and Credit Derivative Markets (Jan Ericsson, Joel Reneby and Hao Wang)
- Applying the Concept:
- The Default Risk of Swaps (Ian A Cooper and Antonio S Mello)
- Economic Evaluation of Remuneration from Patents and Technology Transfers (Dan Galai and Yael Ilan)
- Credit Risk Derivatives (Sanjiv Ranjan Das)
- Analytic Pricing of Employee Stock Options (Jakša Cvitanić, Zvi Wiener and Fernando Zapatero)
- Stakeholders and the Composition of the Voting Rights of the Board of Directors (Dan Galai and Zvi Wiener)
- The Value of the Freezeout Option (Zohar Goshen and Zvi Wiener)
- Dividends as Contingent Claims:
- Dividend-Paying Stock (Kenneth D Garbade)
- Dividend Policy Relevance in a Levered Firm — The Binomial Case (Dan Galai and Zvi Wiener)
- Volume 4: Contingent Claims Approach for Banks and Sovereign Debt:
- Banking Models:
- An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees: An Application of Modern Option Pricing Theory (Robert C Merton)
- Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model (Ehud I Ronn and Avinash K Verma)
- A Contingent Claim Analysis of a Regulated Depository Institution (Michel Crouhy and Dan Galai)
- Credit Risk and the Deposit Insurance Premium: A Note (Jean Dermine and Fatma Lajeri)
- Contingent Convertibles (CoCos):
- A Structural Model of Contingent Bank Capital (George Pennacchi)
- Contingent Capital with a Capital-Ratio Trigger (Paul Glasserman and Behzad Nouri)
- Pricing Contingent Convertibles: A Derivatives Approach (Jan De Spiegeleer and Wim Schoutens)
- On the Design of Contingent Capital with a Market Trigger (Suresh Sundaresan and Zhenyu Wang)
- International Perspectives and Sovereign Debt:
- Measuring and Analyzing Sovereign Risk with Contingent Claims (Michael T Gapen, Dale F Gray, Cheng Hoon Lim and Yingbin Xiao)
- Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk (Dale F Gray, Robert C Merton and Zvi Bodie)
- A Contingent Claims Analysis of the Subprime Credit Crisis of 2007–2008 (Dale F Gray, Robert C Merton and Zvi Bodie)
- Measuring and Managing Macrofinancial Risk and Financial Stability: A New Framework (Dale F Gray, Robert C Merton and Zvi Bodie)
- Credit Risk Spreads in Local and Foreign Currencies (Dan Galai and Zvi Wiener)
- Finance Meets Macroeconomics: A Structural Model of Sovereign Credit Risk (Emilian Belev and Dan diBartolomeo)
Readership: Graduate students, college and university teachers, researchers and practitioners who are interested in understanding the approaches and methods required to sustain the viability of a corporate enterprise.

Michel Crouhy was, until recently, Head of Research & Development at Natixis Corporate and Investment Banking, a subsidiary of Groupe BPCE (Banques Populaires and Caisses d'Epargne). He is currently a senior advisor in charge of implementing a 'scenario-based stress testing framework' which is fully integrated into the capital and liquidity planning process of the bank. He coordinates cross-asset initiatives in the Natixis's Capital Markets Division. He is also the founder and Chairman of the Board of the Natixis Foundation for Research and Innovation, which promotes and supports academic research and world-class events in the area of mathematical finance and data science.
Prior to this, Crouhy served as Senior Vice President of the Risk Management Division at the Canadian Imperial Bank of Commerce (CIBC), in charge of risk analytics, model vetting and model risk management, operational risk, economic capital attribution and customer behavior analytics. In addition to his career in the industry, Crouhy was a professor of finance at the HEC School of Management in Paris, and a visiting professor at the Wharton School of the University of Pennsylvania and at the University of California, Los Angeles.
Crouhy is a founding member of PRMIA, the Professional Risk Managers' International Association. He is a member of the Research Advisory Council of the Global Risk Institute in Financial Services and of the Credit Committee of the International Association of Financial Engineers (IAFE). He is a member of the Scientific Executive Board of the 'Institut Louis Bachelier'. He is the author and co-author of several books, the most recent being Risk Management (McGraw-Hill, 2001) and The Essentials of Risk Management (McGraw-Hill, second edition, 2014). Crouhy holds a PhD from the Wharton School of the University of Pennsylvania, and a Honoris Causa degree from the University of Montreal.

Dan Galai is the former Dean of the School of Business Administration, the Hebrew University of Jerusalem and the Abe Gray Emeritus Professor of Finance and Business Administration. He was a visiting Professor of Finance at INSEAD, the University of California, Los Angeles, the Stern School of Business, NYU, and the MBS at the University of Melbourne. In the summer of 2008, he served as a Visiting Scholar at the IMF. He has also taught at the University of Chicago and at the University of California, Berkeley. Dr Galai holds a PhD from the University of Chicago and undergraduate and graduate degrees from the Hebrew University.
He has served as a consultant for the Chicago Board Options Exchange (CBOE) and the NYSE American (formerly the American Stock Exchange) as well as for major banks. He co-invented the volatility index based on traded index option prices. He is a recipient of the First Annual Pomerance Prize presented by the CBOE for excellence in options research.
Galai is co-author of the books, Risk Management (McGraw-Hill, 2001), The Essentials of Risk Management (McGraw-Hill, 2nd edition in 2014) and How to Create a Successful Business Plan (World Scientific Publishers, 2016).
Dr Galai is a founder and the Chairman of the Board of Sigma Investment House Ltd. and a co-founder of MutualArt Inc., a financial services company, which provides pension-like benefits to select artists worldwide. In addition, he serves on the boards of several start-up companies.

Zvi Wiener is the Dean of the Jerusalem School of Business Administration at the Hebrew University of Jerusalem. He is an expert in risk management, financial engineering and the valuation of complex financial products. He is one of the founders of PRMIA (Professional Risk Managers' International Association), has served as a co-chair of the organization's worldwide Education and Standards Committee, and is currently a co-director of PRMIA, Israel.
His research appears in various journals, including The Journal of Finance, The Review of Financial Studies, the Journal of Banking and Finance, The Journal of Derivatives, and the Journal of Corporate Finance, to mention a few. He was awarded the Teva Prize for research on dividend policy in 2014, and the PRMIA award for Outstanding Service and Leadership in 2012, as well as the Alon Fellowship and Rothschild Fellowship. Dr Wiener was awarded five competitive grants from the Israel Academy of Sciences and Humanities (ISF) as well as several other research grants.
Zvi Wiener has vast experience in consulting. He served as a consultant to the Israeli Ministry of Finance, the Ministry of Defense, the Bank of Israel, the Israel Securities Authority, the Tel Aviv Stock Exchange, credit rating agencies, banks, insurance companies and pension funds, as well as to leading law firms.