This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.
Table of Contents
1. Introduction
2. Pricing Financial Contracts Subject to Multiple Credit Risks
2.1. Risky valuation without collateralization
2.2. Risky valuation with collateralization
3. Numerical Results
4. Conclusion
Research Objectives and Topics
This paper develops a new valuation framework for credit default swap (CDS) contracts that explicitly accounts for the credit risks of the buyer, the seller, and the reference entity. The study addresses the limitations of standard models that assume conditional independence and highlights how default dependencies and collateralization significantly influence asset pricing and financial stability.
- Modeling default dependencies using the new statistic "comrelation".
- Evaluating the impact of collateralization on counterparty risk in CDS markets.
- Pricing multilateral defaultable financial contracts.
- Sensitivity analysis of CDS premia regarding joint credit quality and default correlations.
- Investigating why full collateralization does not eliminate counterparty risk for CDS contracts.
Excerpt from the Book
Pricing Financial Contracts Subject to Multiple Credit Risks
In the reduced-form approach, the stopping (or default) time τ_i of firm i is modeled as a Cox arrival process (also known as a doubly stochastic Poisson process) whose first jump occurs at default and is defined by,
τ_i = inf {t: ∫₀ᵗ h_i(s, Z_s)ds ≥ H_i}
where h_i(t) or h_i(t, Z_t) denotes the stochastic hazard rate or arrival intensity dependent on an exogenous common state Z_t, and H_i is a unit exponential random variable independent of Z_t.
It is well-known that the survival probability from time t to s in this framework is defined by p_i(t,s) := P_i(τ > s | t, Z_t) = exp(-∫ₜˢ h_i(u)du). The default probability for the period (t, s) in this framework is given by q_i(t,s) := P_i(τ ≤ s | t, Z_t) = 1 - p_i(t,s) = 1 - exp(-∫ₜˢ h_i(u)du).
Summary of Chapters
1. Introduction: Discusses existing default models and the need to move beyond the assumption of conditional independence to explicitly model default relationships in credit portfolios.
2. Pricing Financial Contracts Subject to Multiple Credit Risks: Introduces the mathematical framework for valuing defaultable contracts, including the concepts of comvariance and comrelation, and provides specific propositions for CDS valuation both with and without collateral.
3. Numerical Results: Presents quantitative analyses using the CIR model to study how default correlations, comrelations, and counterparty credit quality impact CDS premia.
4. Conclusion: Summarizes the key findings, emphasizing that collateralization effectively mitigates bilateral risks but may fail for multilateral risks, and suggests that standard models often underestimate credit risk.
Keywords
valuation model, credit risk modeling, collateralization, correlation, CDS, comvariance, comrelation, counterparty risk, default dependency, financial contagion, derivative pricing, credit spread, Cox-Ingersoll-Ross model, risk management, multilateral default.
Frequently Asked Questions
What is the primary focus of this research paper?
The paper focuses on creating a new framework for valuing credit default swaps (CDS) by considering the credit risks of all three involved parties: the protection buyer, the protection seller, and the reference entity.
What are the central thematic fields addressed?
The core themes include credit risk modeling, the impact of default correlations and multivariate statistical relationships (comrelation) on asset pricing, and the limitations of collateralization in reducing counterparty risk.
What is the primary goal or research question?
The primary goal is to demonstrate that default dependencies significantly impact CDS premia and to prove that full collateralization is insufficient to completely eliminate counterparty risk in the CDS market.
Which scientific methods are employed?
The author uses a reduced-form modeling approach, introduces the statistical concept of "comrelation" for multiple variables, and utilizes regression-based Monte-Carlo simulations to derive numerical results.
What content is covered in the main body?
The main body details the mathematical formulation of default processes, introduces the valuation framework via propositions, and provides an extensive numerical analysis comparing various credit quality scenarios and sensitivity tests.
Which keywords characterize the work?
Key terms include CDS valuation, comrelation, counterparty risk, collateralization, and default dependency.
Does the model support scenarios with more than three parties?
Yes, the author explicitly mentions that the methodology can be extended to cases where the number of parties n is 4 or greater using a generating function for n-variate Bernoulli distributions.
Why does the author claim that full collateralization fails to eliminate risk?
The model shows that because CDS values can change abruptly with large jumps and involve more risk factors than standard interest rate swaps, the collateral amount can fall short of the required protection in times of market distress.
- Citation du texte
- Alan White (Auteur), 2018, Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization, Munich, GRIN Verlag, https://www.grin.com/document/417474
