Counterparty Credit Risk and Credit Value Adjustment

A Continuing Challenge for Global Financial Markets

Jon Gregory

• Publisher: Wiley
• Year: 2012
• Print ISBN: 9781118316672
• eBook ISBN: 9781118316665
• Edition: 1
• Topic: Business
• Subtopic: Finance
• Index: Business

A practical guide to counterparty risk management and credit value adjustment from a leading credit practitioner

Please note that this second edition of Counterparty Credit Risk and Credit Value Adjustment has now been superseded by an updated version entitled The XVA Challenge: Counterparty Credit Risk, Funding, Collateral and Capital.

Since the collapse of Lehman Brothers and the resultant realization of extensive counterparty risk across the global financial markets, the subject of counterparty risk has become an unavoidable issue for every financial institution. This book explains the emergence of counterparty risk and how financial institutions are developing capabilities for valuing it. It also covers portfolio management and hedging of credit value adjustment, debit value adjustment, and wrong-way counterparty risks. In addition, the book addresses the design and benefits of central clearing, a recent development in attempts to control the rapid growth of counterparty risk. This uniquely practical resource serves as an invaluable guide for market practitioners, policy makers, academics, and students.

Section III: Credit Value Adjustment

In this section, we discuss the pricing of counterparty credit risk via credit value adjustment (CVA). CVA is becoming an increasingly important concept for banks and other financial institutions, driven by accounting standards, regulation and best practice. In its most simple form, CVA quantification is relatively simple, respecting just a combination of exposure and default probability as already discussed in Chapters 9 and 10. Nevertheless, being able to compute CVA in an efficient, accurate and timely fashion represents a number of challenges. Chapter 12 will cover the basics of CVA and methods for quantifying CVA. Of particular importance is that CVA is increasingly commonly calculated with reference to market parameters (risk-neutral) rather than real-world (e.g., historical) ones. This means that daily, and even intradaily, CVA calculations are increasingly becoming the norm. The pricing of new trades is often done with real-time incremental CVA calculations, which are challenging to make accurately. The market standard calculations and methodology for CVA will be described.

Another component of counterparty credit risk is debt value adjustment (DVA), which is the subject of Chapter 13. DVA is a mirror image of CVA as it represents the pricing of counterparty risk considering an institution's own default. This might sound somewhat counterintuitive but is a common practice, which is supported by accountancy standards. DVA has some theoretically nice properties as it provides a symmetry whereby market participants can agree on counterparty risk pricing. It also, however, has some difficult side-effects, which have sometimes formed a criticism of DVA (for example, an institution reports greater profits when their credit quality deteriorates). Indeed, some of the perceived negative aspects of DVA have led to it being excluded from Basel III capital rules (covered later in Chapter 17). We will go through the basics of DVA with examples and summarise the positive and negative factors behind it.

The calculation of CVA and DVA is done with respect to a “risk-free” value. Pricing financial instruments such as derivatives has always been relatively complex. However, certain aspects of valuation have been considered rather trivial. One of these is the use of LIBOR as a discount rate. In the good old days, a vanilla derivative such as a swap could be valued almost trivially by discounting cash flows on the LIBOR curve. Nowadays, the problem is much more complex and involves “OIS” or “dual-curve” discounting. Since this problem is related to counterparty risk valuation, we discuss valuation issues in Chapter 14. This chapter also discusses the implication of funding costs on transactions via FVA, which is an additional component, similar in many aspects to CVA. Like risk-free valuation, funding is a peripheral subject to counterparty risk, but is important to cover especially in understanding the relationship between DVA and funding. It also discusses the impact of collateral (CollVA) on valuation.

The valuation of counterparty credit risk often makes the assumption that exposure (market risk) and default probability (credit risk) are independent. This is a convenient assumption that makes much of CVA (and also DVA and FVA) quantification achievable. Unfortunately, this assumption is almost inevitably always incorrect as independence of financial variables is an idealistic assumption, especially during volatile periods and crises. Hence, there is a need to assess wrong-way (and right-way) risk, which arises from the dependence between exposure and default probability. Chapter 15 is dedicated to this, where we will discuss practical ways in which CVA approaches can incorporate wrong-way risk. Wrong-way risk in different asset classes will be considered and the impact of collateral on mitigating wrong-way risk will be described. Consideration will be given to the impact of wrong-way risk on central counterparties, which is an important topic given the central clearing of credit derivative products.

Chapter 9

Quantifying Credit Exposure

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The trouble with our times is that the future is not what it used to be.

Paul Valery (1871–1945)

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9.1 Introduction

In this chapter, we present an overview of the various methods to quantify exposure. These vary from the simple but crude to the more complex generic approach of Monte Carlo simulation. This latter approach forms the majority of the discussion, as it is the most complex and has rapidly become a standard. We will define, in detail, the methodology for exposure quantification via Monte Carlo simulation, including a discussion of the approaches to modelling risk factors in different asset classes and their co-dependencies.

To illustrate many of the concepts here and in the previous chapter, we will then show a number of real examples, looking in particular at the impact of netting and collateral as well as other relevant effects.

At the heart of the problem of quantifying exposure lies a balance between the following two effects:

• As we look into the future, we become increasingly uncertain about market variables. Hence, risk increases as we move through time.
• Many financial instruments have cash flows that are paid over time, and this tends to reduce the risk profiles as the instruments “amortise” through time.

Nevertheless, the practical calculation of exposure involves choosing a balance between sophistication and operational considerations.

9.2 Methods for Quantifying Credit Exposure

9.2.1 Add-Ons

The simplest approach to approximate future exposure is to take the current positive exposure and add a component that represents the uncertainty of the PFE in the future. This type of approach is highly simplistic and forms the basis of the Basel I capital rules (discussed in Section 17.3.1), often known as the “current exposure (CEM)” approach. At the trade level, the “add-on” component should account for:

• the time horizon in question;
• the volatility of the underlying asset class.

For example, longer time horizons will require larger add-ons, and volatile asset classes such as FX and commodities should attract larger add-ons. Add-on approaches are fast and allow exposures to be pre-calculated and distributed via simple “grids”. Such grids allow a very quick look-up of the PFE impact of a new trade.

However, an add-on approach does not typically account for more subtle effects, including:

• the specifics of the transaction in question (currency, specifics of cash flows);
• if the transaction has a mark-to-market very far from zero (other than the addition of this mark-to-market when it is positive);
• netting;
• collateral.

It is difficult to incorporate such effects except with rather crude rules (for example, Basel I allows 60% of current netting benefit to apply to future exposure). More sophisticated add-on methodologies have been developed (e.g., Rowe, 1995; Rowe and Mulholland, 1999), although the increased complexity of such approaches must be balanced against the power afforded by a more generic method such as Monte Carlo simulation.

9.2.2 Semi-Analytical Methods

Semi-analytical methods are generally more sophisticated than the simple add-on approaches but still require some approximations. Their advantage lies in avoiding the time-consuming process of Monte Carlo simulation. A semi-analytical method will generally be based on:

• making some simple assumption regarding the risk factor(s) driving the exposure;
• finding the distribution of the exposure as defined by the above risk factor(s);
• calculating a semi-analytical approximation to a risk metric for that exposure distribution.

Some simple and general analytical expressions were described in the last chapter and formulas can be found in the appendices.

More product-specific analytical formulas¹ can be found in, for example, Sorensen and Bollier (1994) who show that the ...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Acknowledgements
• List of Spreadsheets
• List of Appendices
• Section I: Introduction
• Section II: Mitigation of Counterparty Credit Risk
• Section III: Credit Value Adjustment
• Section IV: Managing Counterparty Credit Risk
• References
• Index