This paper presents a new model for pricing over the counter (OTC) derivatives subject to collateralization. It allows for collateral posting adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives.
Using a unique dataset, the author found empirical evidence that credit risk alone is not overly important in determining credit-related spreads. Only accounting for both collateral arrangement and credit risk can sufficiently explain unsecured credit costs. This finding suggests that failure to properly account for collateralization may result in significant mispricing of derivatives. The author also empirically gauges the impact of collateral agreements on risk measurements. The findings indicate that there are important interactions between market and credit risk.
Table of Contents
Pricing Collateralized Financial Derivatives
Empirical Results
Impact of collateralization on swap rate
Impact of collateralization on credit risk
Impact of collateralization on market risk
Conclusion
Appendix
Research Objectives and Core Topics
This paper develops a new pricing model for OTC derivatives that explicitly incorporates the effects of collateralization and bankruptcy laws, aiming to quantify how collateral agreements influence swap rates, counterparty credit risk (CVA), and market risk (VaR).
- Modeling collateralized OTC derivative pricing structures
- Empirical evaluation of the impact of collateralization on swap premium spreads
- Analysis of the relationship between collateralization and Credit Value Adjustment (CVA)
- Assessment of the interaction between collateralization and market risk (VaR)
- Integration of market and credit risk frameworks
Excerpt from the Book
Pricing Collateralized Financial Derivatives
A CSA is a legal document that regulates collateral posting. It specifies a variety of terms including threshold, independent amount, and minimum transfer amount (MTA). A threshold is the unsecured credit exposure that a party is willing to bear. A MTA is used to avoid the workload associated with a frequent transfer of insignificant collateral amounts. An independent amount plays the same role as an initial margin or haircut. We define the effective collateral threshold as the threshold plus the MTA. Collateral is called as soon as the mark-to-market (MTM) value rises above the effective threshold.
There are three types of collateralization: partial, over or full. A positive effective threshold corresponds to partial-collateralization where the posting of collateral is less than the MTM value. A negative effective threshold represents over-collateralization where the posting of collateral is greater than the MTM value. A zero-value effective threshold equates with full-collateralization where the posting of collateral is equal to the MTM value. Our generic model is applicable to all the types.
Summary of Chapters
Pricing Collateralized Financial Derivatives: Introduces a mathematical framework for valuing collateralized derivatives that accounts for the legal structure of Credit Support Annexes (CSAs) and bankruptcy laws.
Empirical Results: Presents an indirect empirical study using proprietary data to test the model's performance in explaining swap premium spreads, CVA, and Value at Risk.
Impact of collateralization on swap rate: Examines how collateral and credit risk interact to determine market swap spreads, finding that joint modeling significantly improves explanatory power.
Impact of collateralization on credit risk: Demonstrates that collateral posting reduces CVA and identifies a negative correlation between collateralization and counterparty credit risk.
Impact of collateralization on market risk: Analyzes the VaR of portfolios under different collateral conditions, revealing that collateralization effectively mitigates market risk exposure.
Conclusion: Summarizes the key findings, emphasizing that an integrated approach to market and credit risk, driven by the inclusion of collateralization, is essential for accurate derivative valuation.
Appendix: Provides the detailed mathematical proofs and derivations for the propositions presented in the pricing model.
Keywords
collateralization, asset pricing, plumbing of financial system, swap premium spread, CVA, VaR, interaction between market and credit risk, OTC derivatives, credit default swap, counterparty risk, bankruptcy law, Libor market model, backward induction, risk-adjusted discount ratio
Frequently Asked Questions
What is the primary focus of this research?
The paper focuses on developing a new pricing model for over-the-counter (OTC) derivatives that integrates collateralization agreements, providing a framework to account for the impact of counterparty credit risk and legal bankruptcy structures.
What are the central themes discussed in the paper?
The core themes include the mathematical modeling of collateralized derivatives, the empirical analysis of swap premium spreads, the calculation of Credit Value Adjustment (CVA), and the assessment of Value at Risk (VaR) in the presence of collateral.
What is the main objective of the proposed pricing model?
The goal is to back out the market price of collateralized contracts by modeling the collateral process directly based on the fundamental principles and legal structure of Credit Support Annexes (CSAs).
Which scientific methods are employed in the study?
The research uses a reduced-form modeling framework, the Libor Market Model (LMM) lattice for pricing, backward induction for valuation, and linear regression analysis on proprietary datasets to empirically validate the model.
What does the empirical analysis of the main body cover?
It covers the comparison of model-implied prices against dealer-quoted market prices, the marginal impact of credit risk on spreads, and the joint effect of credit risk and collateralization on both CVA and VaR.
Which keywords best characterize this work?
Key terms include collateralization, swap premium spread, CVA, VaR, OTC derivatives, and the interaction between market and credit risk.
How does the author define the relationship between collateralization and market risk?
The author finds a negative correlation, suggesting that contrary to some prevailing market beliefs, collateral posting can actually reduce VaR and mitigate market risk exposure.
What is the significance of the "effective threshold" in this model?
The effective threshold—defined as the threshold plus the Minimum Transfer Amount (MTA)—determines the level of collateralization (partial, full, or over) and is critical for assessing unsecured credit exposure.
What does the study conclude about credit risk and swap spreads?
The study concludes that counterparty credit risk alone is insufficient to explain market spreads; a combination of both credit risk and collateralization is required to adequately account for unsecured credit costs.
- Quote paper
- Tim Xiao (Author), 2020, Pricing of Collateralized Over the Counter Derivatives, Munich, GRIN Verlag, https://www.grin.com/document/916174
