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The xVA Challenge

Counterparty Credit Risk, Funding, Collateral and Capital

Third Edition

Jon Gregory

This edition first published 2015
© 2015 John Wiley & Sons, Ltd
First edition published 2009, second edition published 2012 by John Wiley & Sons, Ltd

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ISBN 978-1-119-10941-9 (hbk)      ISBN 978-1-119-10943-3 (ebk)
ISBN 978-1-119-10942-6 (ebk)      ISBN 978-1-119-10944-0 (ebk)

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Set in 10/12pt Times by Sparks – www.sparkspublishing.com

To Sylvia, Mimsie, Stella, Cara, Eliza-Joy, Stevie, Peach, Jim, Ginnie, George and Christy

Contents

Lists of Spreadsheets

Lists of Appendices

Acknowledgements

About the Author

1 Introduction

2 The Global Financial Crisis

2.1 Pre-crisis

2.2 The crisis

2.3 Regulatory reform

2.4 Backlash and criticisms

2.5 A new world

Notes

3 The OTC Derivatives Market

3.1 The derivatives market

3.2 Derivative risks

3.3 Risk management of derivatives

Notes

4 Counterparty Risk

4.1 Background

4.2 Components

4.3 Control and quantification

4.4 Beyond CVA

4.5 Summary

Notes

5 Netting, Close-out and Related Aspects

5.1 Introduction

5.2 Default, netting and close-out

5.3 Multilateral netting and trade compression

5.4 Termination features and resets

5.5 Summary

Notes

6 Collateral

6.1 Introduction

6.2 Collateral terms

6.3 Mechanics of collateral

6.4 Collateral and funding

6.5 Collateral usage

6.6 The risks of collateral

6.7 Regulatory collateral requirements

6.8 Converting counterparty risk into funding liquidity risk

6.9 Summary

Notes

7 Credit Exposure and Funding

7.1 Credit exposure

7.2 Metrics for exposure

7.3 Factors driving exposure

7.4 The impact of netting and collateral on exposure

7.5 Funding, rehypothecation and segregation

7.6 Summary

Notes

8 Capital Requirements and Regulation

8.1 Background to Credit Risk Capital

8.2 Current Exposure Method (CEM)

8.3 The Internal Model Method (IMM)

8.4 Standardised Approach for Counterparty Credit Risk (SA-CCR)

8.5 Comparison of EAD Methods

8.6 Basel III

8.7 CVA Capital Charge

8.8 Other Important Regulatory Requirements

8.9 Summary

Notes

9 Counterparty Risk Intermediation

9.1 Introduction

9.2 SPVs, DPCs, CDPCs and monolines

9.3 Central counterparties

9.4 Summary

Notes

10 Quantifying Credit Exposure

10.1 Introduction

10.2 Methods for quantifying credit exposure

10.3 Monte Carlo methodology

10.4 Real-world or risk-neutral

10.5 Model choice

10.6 Examples

10.7 Allocating exposure

10.8 Summary

Notes

11 Exposure and the Impact of Collateral

11.1 Overview

11.2 Margin period of risk

11.3 Numerical examples

11.4 Initial margin

11.5 Summary

Notes

12 Default Probabilities, Credit Spreads and Funding Costs

12.1 Overview

12.2 Default probability

12.3 Credit curve mapping

12.4 Generic curve construction

12.5 Funding curves and capital costs

12.6 Summary

Notes

13 Discounting and Collateral

13.1 Overview

13.2 Discounting

13.3 Beyond perfect collateralisation

13.4 Collateral valuation adjustments

13.5 Summary

Notes

14 Credit and Debt Value Adjustments

14.1 Overview

14.2 Credit value adjustment

14.3 Impact of credit assumptions

14.4 CVA allocation and pricing

14.5 CVA with collateral

14.6 Debt value adjustment

14.7 Summary

Notes

15 Funding Value Adjustment

15.1 Funding and derivatives

15.2 Funding value adjustment

15.3 The practical use of FVA

15.4 Summary

Notes

16 Margin and Capital Value Adjustments

16.1 Overview

16.2 Margin value adjustment

16.3 Capital value adjustment

16.4 Summary

Notes

17 Wrong-way Risk

17.1 Overview

17.2 Overview of wrong-way risk

17.3 Quantification of wrong-way risk

17.4 Wrong-way risk modelling approaches

17.5 Summary

Notes

18 xVA Management

18.1 Introduction

18.2 The role of an xVA desk

18.3 Hedging xVA

18.4 xVA systems

18.5 Summary

Notes

19 xVA Optimisation

19.1 Overview

19.2 Market practice

19.3 Examples

19.4 Costs and the balance of xVA terms

19.5 xVA optimisation

19.6 Summary

Notes

20 The Future

Glossary

References

Index

EULA

List of Tables

Chapter 4

Table 4.1

Chapter 5

Table 5.1

Chapter 6

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Table 6.6

Table 6.7

Table 6.8

Chapter 7

Table 7.1

Table 7.2

Table 7.3

Table 7.4

Chapter 8

Table 8.1

Table 8.2

Table 8.3

Table 8.4

Chapter 9

Table 9.1

Chapter 10

Table 10.1

Table 10.2

Table 10.3

Table 10.4

Chapter 11

Table 11.1

Table 11.2

Chapter 12

Table 12.1

Table 12.2

Table 12.3

Table 12.4

Table 12.5

Chapter 13

Table 13.1

Table 13.2

Chapter 14

Table 14.1

Table 14.2

Table 14.3

Table 14.4

Table 14.5

Table 14.6

Table 14.7

Chapter 15

Table 15.1

Table 15.2

Table 15.3

Table 15.4

Table 15.5

Chapter 16

Table 16.1

Table 16.2

Chapter 17

Table 17.1

Table 17.2

Table 17.3

Chapter 18

Table 18.1

Table 18.2

Table 18.3

Chapter 19

Table 19.1

Table 19.2

Table 19.3

Table 19.4

Table 19.5

Table 19.6

List of Illustrations

Chapter 3

Figure 3.1 Total outstanding notional of OTC and exchange-traded derivatives transactions. The figures cover interest rate, foreign exchange, equity, commodity and credit derivative contracts. Note that notional amounts outstanding are not directly comparable to those for exchange-traded derivatives, which refer to open interest or net positions, whereas the amounts outstanding for OTC markets refer to gross positions, i.e., without netting.

Figure 3.2 Breakdown of different types of derivatives by total notional.

Figure 3.3 Management of derivative transactions by the Lehman Brothers estate.

Figure 3.4 Illustration of the value-at-risk (VAR) concept at the 99% confidence level. The VAR is 125, since the chance of a loss greater than this amount is no more than 1%.

Figure 3.5 Distribution with the same VAR as Figure 3.4.

Chapter 4

Figure 4.1 Illustration of pre-settlement and settlement risk. Note that the settlement period is normally short (e.g., hours) but can be much longer in some cases.

Figure 4.2 Split of OTC gross outstanding notional by product type as of June 2014.

Figure 4.3 Split of CVA by asset class (average over all respondents).

Figure 4.4 Illustration of the classic end-user counterparty risk setup.

Figure 4.5 Illustration of the classic bank setup.

Figure 4.6 Illustration of the use of PFE and credit limits in the control of counterparty risk.

Figure 4.7 High-level illustration of the complimentary use of CVA and credit limits to manage counterparty risk.

Figure 4.8 Illustration of CDS hedging in order to increase a credit limit (this assumes the maturity of the CDS contract is longer than the maximum time shown)..

Figure 4.9 Illustration of the role of a CVA desk (xVA desk) in a bank.

Figure 4.10 Illustration of the lifetime cost of an OTC derivative. Note that this representation is general; in reality, thresholds are often zero or infinity.

Figure 4.11 Generic illustration of an xVA term. Note that the some xVA terms represent benefits and not costs and would appear on the negative y-axis.

Figure 4.12 Illustration of the role of xVA adjustments.

Chapter 5

Figure 5.1 Illustration of the need for netting in bilateral markets.

Figure 5.2 Illustration of the impact of payment netting.

Figure 5.3 Illustration of the impact of close-out netting. In the event of the default of party A, without netting, party B would need to pay 200 to party A and would not receive the full amount of 140 owed. With netting, party B would simply pay 60 to party A and suffer no loss.

Figure 5.4 Illustration of the impact of netting on OTC derivatives exposure. The netting benefit (right hand y-axis) is defined by dividing the gross credit exposure by the gross market value and subtracting this ratio from 100%.

Figure 5.5 Illustration of the potential exposure reduction offered by multilateral netting. The black and grey exposures indicate positions in contractually identical (and therefore fungible) transactions, differing only in notional amount. The exposures in grey are removed completely, whilst those in black are reduced by ten units.

Figure 5.6 Illustration of a simple “market” made up of positions in fungible (interchangeable) contracts.

Figure 5.7 Illustration of using trilateral netting between counterparties 2, 3 and 4 to reduce the overall notional of the system shown in Figure 5.6.

Figure 5.8 Illustration of two possible final results of compressing the original market in Figure 5.6 leading to total notionals of 130 (left-hand side) and 110 (right-hand side).

Figure 5.9 Illustration of the impact of reset features on the exposure of a long-dated cross-currency swap. Resets are assumed to occur quarterly.

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