Counterparty Credit Risk, Collateral and Funding

With Pricing Cases For All Asset Classes

Damiano Brigo, Massimo Morini, Andrea Pallavicini

• Publisher: Wiley
• Year: 2013
• Print ISBN: 9780470748466
• eBook ISBN: 9780470661789
• Edition: 1
• Topic: Business
• Subtopic: Finance
• Index: Business

The book's content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular 'concrete' financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity.

The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a 'feel' for applying sophisticated mathematics and stochastic calculus to solve practical problems.

The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation.

Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered.

Part I

COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING

1

Introduction

This chapter is based on the summary given in Brigo (2011b) [34].

In this introductory chapter we present a dialogue that clarifies the main issues dealt with in the book. This chapter is also a stand-alone informal guide to problems in counterparty risk valuation and measurement, with references for readers who may wish to pursue further the different aspects of this type of credit risk. Later chapters in the book will provide in-depth studies of all aspects of counterparty risk.

1.1 A DIALOGUE ON CVA

Although research on counterparty risk pricing started way back in the nineties, with us joining the effort back in 2002, the different aspects of counterparty credit risk exploded after the start of the global financial crisis in 2007. In less than four years we have seen the emergence of a number of features that the market operators are struggling to account for with consistency. Further, the several possible definitions and methodologies for counterparty risk may create confusion. This dialogue is meant to provide an informal guide to the different aspects of counterparty risk. It is in the form of questions and answers between a CVA expert and a newly hired colleague, and provides detailed references for investigating the different areas sketched here in more detail.

1.2 RISK MEASUREMENT: CREDIT VaR

Q: [Junior colleague, he is looking a little worried] I am new in this area of counterparty risk, and I am struggling to understand the different measures and metrics. Could you start by explaining generally what counterparty risk is?

A: [Senior colleague, she is looking at the junior colleague reassuringly.] The risk taken on by an entity entering an Over-The-Counter (OTC) contract with one (or more) counterparty having a relevant default probability. As such, the counterparty might not respect its payment obligations.

Q: What kind of counterparty risk practices are present in the market?

A: Several, but most can be divided into two broad areas. Counterparty risk measurement for capital requirements, following Basel II, or counterparty risk from a pricing point of view, when updating the price of instruments to account for possible default of the counterparty. However, the distinction is now fading with the advent of Basel III.

Q: [Shifts nervously] Let us disentangle this a little, I am getting confused.

A: Fine. Where do we start from?

Q: Let us start from Counterparty Risk Measurement for Capital Requirements. What is that?

A: It is a risk that one bank faces in order to be able to lend money or invest towards a counterparty with relevant default risk. The bank needs to cover for that risk by setting capital aside, and this can be done after the risk has been measured.

Q: You are saying that we aim at measuring that risk?

A: Indeed, and this measurement will help the bank decide how much capital the bank should set aside (capital requirement) in order to be able to face losses coming from possible defaults of counterparties the bank is dealing with.

Q: Could you make an example of such a measure?

A: A popular measure is Value at Risk (VaR). It is basically a percentile on the loss distribution associated with the position held by the bank, over a given time horizon. More precisely, it is a percentile (say the 99.9th percentile) of the initial value of the position minus the final value at the risk horizon, across scenarios.

Q: Which horizon is usually taken?

A: When applied to default risk the horizon is usually one year and this is called “Credit VaR (CrVaR)”. If this is taken at the 99.9-th percentile, then you have a loss that is exceeded only in 1 case out of 1,000. The Credit VaR is either the difference of the percentile from the mean, or the percentile itself. There is more than one possible definition.

Q: Is this a good definition of credit risk?

A: [Frowning] Well what does “good” really mean? It is not a universally good measure. It has often been criticized, especially in the context of pure market risk without default, for lack of sub-additivity. In other terms, it does not always acknowledge the benefits of diversification, in that in some paradoxical situations the risk of a total portfolio can be larger than the sum of the risks in a single position. A better measure from that point of view would be expected shortfall, known also as tail VaR, conditional VaR, etc.

Q: And what is that?

A: This is loosely defined as the expected value of the losses beyond the VaR point. But this need not concern us too much at present.

Q: Fine. How is Credit VaR typically calculated?

A: Credit VaR is calculated through a simulation of the basic financial variables underlying the portfolio under the historical probability measure, commonly referred to as P, up to the risk horizon. The simulation also includes the default of the counterparties. At the risk horizon, the portfolio is priced in every simulated scenario of the basic financial variables, in...

Table of contents

• Cover
• About The Book
• Series
• Title Page
• Copyright
• Ignition
• Abbreviations and Notation
• Part I: Counterparty Credit Risk, Collateral and Funding
• Part II: Pricing Counterparty Risk: Unilateral CVA
• Part III: Advanced Credit and Funding Risk Pricing
• Bibliography
• Index