The xVA Challenge E-Book

Jon Gregory

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Series
• Sprache: Englisch

Seitenzahl: 1440

Veröffentlichungsjahr: 2020

Beschreibung

A thoroughly updated and expanded edition of the xVA challenge The period since the global financial crisis has seen a major re-appraisal of derivatives valuation, generally expressed in the form of valuation adjustments ('xVAs'). The quantification of xVA is now seen as fundamental to derivatives pricing and valuation. The xVA topic has been complicated and further broadened by accounting standards and regulation. All users of derivatives need to have a good understanding of the implications of xVA. The pricing and valuation of the different xVA terms has become a much studied topic and many aspects are in constant debate both in industry and academia. * Discussing counterparty credit risk in detail, including the many risk mitigants, and how this leads to the different xVA terms * Explains why banks have undertaken a dramatic reappraisal of the assumptions they make when pricing, valuing and managing derivatives * Covers what the industry generally means by xVA and how it is used by banks, financial institutions and end-users of derivatives * Explains all of the underlying regulatory capital (e.g. SA-CCR, SA-CVA) and liquidity requirements (NSFR and LCR) and their impact on xVA * Underscores why banks have realised the significant impact that funding costs, collateral effects and capital charges have on valuation * Explains how the evolution of accounting standards to cover CVA, DVA, FVA and potentially other valuation adjustments * Explains all of the valuation adjustments - CVA, DVA, FVA, ColVA, MVA and KVA - in detail and how they fit together * Covers quantification of xVA terms by discussing modelling and implementation aspects. Taking into account the nature of the underlying market dynamics and new regulatory environment, this book brings readers up to speed on the latest developments on the topic.

Leseprobe

Table of Contents

Cover

List of Spreadsheets

List of Appendices

Acknowledgements

About the Author

Section 1: Basics

1 Introduction

2 Derivatives

2.1 INTRODUCTION

2.2 THE DERIVATIVES MARKET

2.3 DERIVATIVE RISKS

2.4 SYSTEMIC RISK OF DERIVATIVES

2.5 THE GLOBAL FINANCIAL CRISIS AND CENTRAL CLEARING OF OTC DERIVATIVES

2.6 DERIVATIVES RISK MODELLING

NOTES

3 Counterparty Risk and Beyond

3.1 COUNTERPARTY RISK

3.2 BEYOND COUNTERPARTY RISK

3.3 COMPONENTS OF XVA

NOTES

4 Regulation

4.1 REGULATION AND THE GLOBAL FINANCIAL CRISIS

4.2 CAPITAL REQUIREMENTS

4.3 LIQUIDITY

4.4 CLEARING AND MARGINING

NOTES

5 What is xVA?

5.1 OVERVIEW

5.2 ANALYSIS OF XVA

5.3 VALUATION

5.4 PRICING

NOTES

Section 2: Risk Mitigation

6 Netting, Close-Out, and Related Aspects

6.1 OVERVIEW

6.2 CASH FLOW NETTING

6.3 VALUE NETTING

6.4 THE IMPACT OF NETTING

NOTES

7 Margin (Collateral) and Settlement

7.1 TERMINATION AND RESET FEATURES

7.2 BASICS OF MARGIN/COLLATERAL

7.3 MARGIN TERMS

7.4 BILATERAL MARGIN REQUIREMENTS

7.5 IMPACT OF MARGIN

7.6 MARGIN AND FUNDING

NOTES

8 Central Clearing

8.1 EVOLUTION OF CENTRAL CLEARING

8.2 MECHANICS OF CENTRAL CLEARING

8.3 CCP RISK MANAGEMENT

8.4 INITIAL MARGIN AND DEFAULT FUNDS

8.5 IMPACT OF CENTRAL CLEARING

NOTES

9 Initial Margin Methodologies

9.1 ROLE OF INITIAL MARGIN

9.2 INITIAL MARGIN APPROACHES

9.3 HISTORICAL SIMULATION

9.4 BILATERAL MARGIN AND SIMM

NOTES

10 The Impact and Risk of Clearing and Margining

10.1 RISKS OF CENTRAL CLEARING

10.2 ANALYSIS OF A CCP LOSS STRUCTURE

10.3 IMPACT OF MARGIN

NOTES

Section 3: Building Blocks

11 Future Value and Exposure

11.1 CREDIT EXPOSURE

11.2 DRIVERS OF EXPOSURE

11.3 AGGREGATION, PORTFOLIO EFFECTS, AND THE IMPACT OF COLLATERALISATION

11.4 FUNDING, REHYPOTHECATION, AND SEGREGATION

NOTES

12 Credit Spreads, Default Probabilities, and LGDs

12.1 DEFAULT PROBABILITY

12.2 CREDIT CURVE MAPPING

12.3 GENERIC CURVE CONSTRUCTION

NOTES

13 Regulatory Methodologies

13.1 OVERVIEW

13.2 CREDIT RISK (DEFAULT RISK) CAPITAL

13.2 CVA (MARKET RISK) CAPITAL

13.4 EXPOSURE CALCULATION METHODOLOGIES

13.5 EXAMPLES

13.6 CENTRAL COUNTERPARTY CAPITAL REQUIREMENTS

NOTES

14 Funding, Margin, and Capital Costs

14.1 BANK FINANCING

14.2 CAPITAL

14.3 FUNDING

NOTES

15 Quantifying Exposure

15.1 METHODS FOR QUANTIFYING EXPOSURE

15.2 EXPOSURE ALLOCATION

15.3 MONTE CARLO METHODOLOGY

15.4 CHOICE OF MODELS

15.5 MODELLING MARGIN (COLLATERAL)

15.6 EXAMPLES

NOTES

Section 4: The xVAs

16 The Starting Point and Discounting

16.1 THE STARTING POINT

16.2 COLVA AND DISCOUNTING

16.3 BEYOND PERFECT COLLATERALISATION – XVA

NOTES

17 CVA

17.1 OVERVIEW

17.2 CREDIT VALUE ADJUSTMENT

17.3 DEBT VALUE ADJUSTMENT

17.4 CVA ALLOCATION

17.5 IMPACT OF MARGIN

17.6 WRONG-WAY RISK

NOTES

18 FVA

18.1 OVERVIEW

18.2 FVA AND DISCOUNTING

18.3 ASYMMETRIC FVA

NOTES

19 KVA

19.1 OVERVIEW

19.2 CAPITAL VALUE ADJUSTMENT (KVA)

19.3 MANAGEMENT OF KVA

19.4 KVA OVERLAPS

NOTES

20 MVA

20.1 OVERVIEW

20.2 INITIAL MARGIN FUNDING COSTS

20.3 MVA

20.4 LINK TO KVA

NOTES

21 Actively Managing xVA and the Role of an xVA Desk

21.1 THE ROLE OF AN XVA DESK

21.2 HEDGING

21.3 OPERATION OF AN XVA DESK

NOTES

Glossary

References

Index

End User License Agreement

List of Tables

Chapter 2

Table 2.1 Comparison between exchange-traded and OTC derivatives.

Chapter 3

Table 3.1 Components of xVA terms.

Chapter 5

Table 5.1 Evolution of xVA treatment.

Table 5.2 Qualitative illustration of the relative importance of xVA terms in...

Table 5.3 Simple LR example.

Chapter 6

Table 6.1 Simple illustration of trade compression for single-name CDS contra...

Table 6.2 ISDA definitions regarding the determination of the net amount owin...

Table 6.3 Illustration of the reduction in exposure from bilateral netting an...

Table 6.4 Illustration of an increase in overall exposure caused by multilate...

Chapter 7

Table 7.1 Illustration of the risk-mitigation benefit of different types of b...

Table 7.2 Comparison of the impact of variation margin in various derivatives...

Table 7.3 Proportion of each type of counterparty transacting under a CSA. So...

Table 7.4 Example of rating-linked margin parameters. This could correspond t...

Table 7.5 Example haircuts in a margin agreement.

Table 7.6 Example margin calculation. No initial margin.

Table 7.7 Example margin calculation with minimum transfer amount (assumed to...

Table 7.8 Example margin calculation with (dynamic) initial margin.

Table 7.9 Comparison of historical margining practices in bilateral and centr...

Table 7.10 Timescales for the implementation of margin requirements for cover...

Table 7.11 Standardised initial margin schedule as defined by BCBS-IOSCO (201...

Table 7.12 Standardised haircut schedule, as defined by BCBS-IOSCO (2015). No...

Chapter 8

Table 8.1 Some significant central counterparties.

Table 8.2 Comparing bilaterally- and centrally-cleared OTC derivative markets...

Table 8.3 Summary of the strengths and weaknesses between higher and lower in...

Chapter 9

Table 9.1 Example of a SPAN calculation. The price scan range is 22,500 and t...

Table 9.2 Example showing the sub-additivity properties of VAR and ES metrics...

Table 9.3 Comparison of historical simulation using absolute and relative ret...

Table 9.4 Estimation of the initial margin of a GBP pay-fixed interest rate s...

Table 9.5 Comparison of initial margin methodologies for interest rate produc...

Table 9.6 Comparison of initial margin methodologies in centrally-cleared and...

Table 9.7 Calculation of weighted sensitivities for two interest rate positio...

Table 9.8 SIMM delta margin for a different combination of interest rate swap...

Table 9.9 Market participants subject to bilateral initial margin requirement...

Chapter 10

Table 10.1 Analysis of different components of the CCP default waterfall.

Table 10.2 Indicative comparison of counterparty risk, funding, and capital c...

Table 10.3 Comparison of bilateral versus central clearing. Note that bilater...

Chapter 11

Table 11.1 Illustration of the impact of aggregation when there is a positive...

Table 11.2 Illustration of the impact of aggregation when there is a negative...

Table 11.3 Illustration of the impact of margin on exposure. The exposure met...

Table 11.4 Impact of margin type on counterparty risk and funding. In this co...

Chapter 12

Table 12.1 Comparison between real-world and risk-neutral default probabiliti...

Table 12.2 Annual default probabilities for an example credit curve using Equ...

Table 12.3 Recovery rates for CDS auctions for some credit events in 2008. Th...

Table 12.4 The universe of key credit indices globally.

Table 12.5 Comparison of different credit spread approaches.

Table 12.6 Example coefficients and implied credit spreads for a simple examp...

Table 12.7 Regions, sectors, and ratings for IHS Markit CDS Enhanced Sector C...

Chapter 13

Table 13.1 Example risk weights under the standardised approach for credit ri...

Table 13.2 Methodologies for the CVA capital charge.

Table 13.3 BA-CVA supervisory risk weights

Table 13.4 The correlation between the credit spread of a counterparty and th...

Table 13.5 Correlations and risk weights for the interest rate delta risk cla...

Table 13.6 Correlations for the counterparty credit spread delta risk class i...

Table 13.7 Capital relief for CVA hedges under different methodologies.

Table 13.8 Add-on factors (%) for the CEM by the remaining maturity and type ...

Table 13.9 SA-CCR parameters.

Table 13.10 Exposure definitions used by BCBS (2005b) compared to the more co...

Table 13.11 Comparison between minimum capital requirements and the leverage ...

Chapter 14

Table 14.1 Key regulatory metrics for capital and funding.

Table 14.2 Regulatory capital requirements pre- and post-GFC.

Table 14.3 Example RFRs.

Chapter 15

Table 15.1 Utilisation components of different xVA terms. See Glossary for de...

Table 15.2 Summary of different EPE decompositions for the simple example in ...

Table 15.3 As Table 15.2, with a third transaction added.

Table 15.4 Assumptions used in classical and improved models for modelling ma...

Chapter 16

Table 16.1 Illustration of ColVA calculation.

Table 16.2 Illustration of ColCA and ColBA calculation.

Table 16.3 Illustration of ColVA calculation.

Table 16.4 CTD valuations using discounting and ColVA adjustments.

Table 16.5 Illustration of the various components of different types of margi...

Chapter 17

Table 17.1 Running CVA calculations.

Table 17.2 CVA for 10-year receive fixed interest rate swap using the three c...

Table 17.3 Upfront CVA and DVA values (in bps) for 10-year interest rate swap...

Table 17.4 Incremental BCVA calculations (bps upfront) for a seven-year USD s...

Table 17.5 Illustration of the breakdown of CVA of an interest rate swap (IRS...

Table 17.6 Upfront CVA and DVA values (in bps) for 10-year uncollateralised a...

Table 17.7 Characteristics of general and specific WWR.

Table 17.8 CDS quotes (mid-market) for Italian sovereign protection in both U...

Chapter 18

Table 18.1 Upfront FVA value for interest rate swaps. The credit spreads and ...

Table 18.2 Upfront CVA and FVA (non-contingent) values for interest rate swap...

Table 18.3 Upfront CVA and FVA (non-contingent) values for interest rate swap...

Table 18.4 Hypothetical upfront xVA prices in bps for different types of coll...

Table 18.5 Valuation adjustments in the no-FVA and FVA regimes.

Table 18.6 Different FVA calculations for the portfolio characterised in Tabl...

Table 18.7 Incremental pricing of a five-year cross-currency swap for symmetr...

Table 18.8 Incremental pricing for a risk-reducing trade according to the pro...

Table 18.9 NSFR invariance incremental pricing for the five-year cross-curren...

Table 18.10 Marginal FVA in symmetric and asymmetric cases for the transactio...

Table 18.11 Total FVA adjustments with and without LCR costs related to a dow...

Table 18.12 Upfront (non-contingent) FVA value for interest rate swaps with a...

Chapter 19

Table 19.1 KVA calculations (in bps upfront) for the 10-year swap using the c...

Table 19.2 CVA and KVA calculations for the 10-year swap on an upfront (basis...

Table 19.3 Standalone and incremental CVA and KVA calculations for the 10-yea...

Table 19.4 Pricing for CVA and KVA under the two stylised frameworks and a mo...

Chapter 20

Table 20.1 Differences between discretionary and regulatory IM.

Table 20.2 IM impact on xVA. Note that regulatory IM must be segregated, but ...

Table 20.3 Differences between FVA and MVA.

Table 20.4 Balanced and directional portfolios of interest rate swaps for IM ...

Table 20.5 Incremental MVA for the five-year swap in the balanced and directi...

Table 20.6 Impact of IM regimes on MVA and KVA.

Chapter 21

Table 21.1 Consideration of xVA terms in different types of transaction.

Table 21.2 Accrual costs in opposition to xVA time decay.

Table 21.3 Example performance breakdown of an xVA desk.

Table 21.4 xVA Greeks for a 100 million notional receive fixed 10-year intere...

Table 21.5 Illustration of the calculation of rehedging costs.

Table 21.6 Summary of market practice with respect to xVA hedging.

Table 21.7 Summary of market practice with respect to hedging CVA (and potent...

Table 21.8 Example P&L explain.

Table 21.9 Eligibility of xVA hedges under current and future CVA regulatory ...

Table 21.10 Different approaches for releasing a KVA profit of 50 units on a ...

List of Illustrations

Chapter 2

Figure 2.1 Illustration of exchange-traded and bilaterally-traded derivative...

Figure 2.2 Illustration of the role of clearing in financial transactions.

Figure 2.3 Clearing in exchange-traded and OTC derivatives.

Figure 2.4 Total outstanding notional of OTC and exchange-traded derivatives...

Figure 2.5 Split of OTC derivative gross outstanding notional by product typ...

Figure 2.6 Total outstanding notional and gross market value of OTC derivati...

Figure 2.7 Breakdown of different types of derivatives by total notional. So...

Figure 2.8 Illustration of the classic end user counterparty risk set-up.

Figure 2.9 Illustration of an institution borrowing via a floating rate loan...

Figure 2.10 Illustration of the classic bank counterparty risk set-up.

Figure 2.11 Management of derivative transactions by the Lehman Brothers est...

Figure 2.12 Illustration of the hedging of a transaction with counterparty A...

Figure 2.13 Share price (in dollars) of the monoline insurers AMBAC and MBIA...

Figure 2.14 Bilateral and centrally-cleared OTC derivatives. Source: Eurex (...

Figure 2.15 Illustration of the value-at-risk (VAR) concept at the 99% confi...

Figure 2.16 Distribution with the same VAR as the distribution in Figure 2.1...

Chapter 3

Figure 3.1 Illustration of pre-settlement and settlement risk. Note that the...

Figure 3.2 Illustration of the spike in exposure created by a cash flow paym...

Figure 3.3 Split of CVA by asset class (average across all respondents). Sou...

Figure 3.4 Example of CVA breakdown by rating and sector. Source: Royal Bank...

Figure 3.5 Illustration of the use of PFE and credit limits in the control o...

Figure 3.6 High-level illustration of the complementary use of CVA and credi...

Figure 3.7 Illustration of CDS hedging in order to increase a credit limit....

Figure 3.8 Illustration of the role of a CVA desk (xVA desk) in a bank.

Figure 3.9 Illustration of the lifetime cost of a portfolio in relation to x...

Figure 3.10 Generic illustration of an xVA term. Note that some xVA terms re...

Figure 3.11 Illustration of the role of valuation adjustments (xVAs). Note t...

Chapter 4

Figure 4.1 Overview of regulatory changes since the GFC that are relevant fo...

Figure 4.2 Expected and unexpected losses.

Figure 4.3 Overview of capital ratios required since 2019.

Chapter 5

Figure 5.1 Overview of valuation adjustments.

Figure 5.2 Nature of xVA with respect to default.

Figure 5.3 Illustration of xVA charges at entry and exit of a transaction.

Chapter 6

Figure 6.1 Illustration of the need for netting in bilateral markets.

Figure 6.2 Illustration of the impact of payment netting.

Figure 6.3 Illustration of settlement risk in a physically-settled FX transa...

Figure 6.4 Illustration of CLS.

Figure 6.5 Illustration of a clearing ring. The equivalent obligations betwe...

Figure 6.6 Illustration of the potential exposure reduction offered by multi...

Figure 6.7 Illustration of a simple ‘market’ made up of positions in fungibl...

Figure 6.8 Illustration of using trilateral netting between counterparties 2...

Figure 6.9 Illustration of two possible final results of compressing the ori...

Figure 6.10 Illustration of the impact of close-out netting. In the event of...

Figure 6.11 Illustration of the determination of valuation in the event of c...

Figure 6.12 Illustration of the determination of valuation in the event of c...

Figure 6.13 Illustration of the determination of valuation in the event of c...

Figure 6.14 Illustration of the concept of set-off.

Figure 6.15 Illustration of the impact of netting on OTC derivatives exposur...

Figure 6.16 Comparison of no netting, bilateral netting, and central clearin...

Figure 6.17 Comparison of no netting, bilateral netting, and partial central...

Figure 6.18 Example of bilateral derivatives netting, including other credit...

Figure 6.19 Example of bilateral derivatives netting, including other credit...

Chapter 7

Figure 7.1 Illustration of the impact of reset features on the exposure of a...

Figure 7.2 Illustration of the impact of reset features on the exposure of a...

Figure 7.3 Illustration of the basic role of margin.

Figure 7.4 Illustration of the classic end user counterparty risk setup show...

Figure 7.5 Illustration of the classic bank setup shown previously in Figure...

Figure 7.6 Illustration of the difference between variation and initial marg...

Figure 7.7 Illustration of the importance of reuse of margin. Party X transa...

Figure 7.8 Illustration of rehypothecation of margin (large dealers only). S...

Figure 7.9 Illustration of the concept of segregation. Party A posts margin ...

Figure 7.10 Breakdown of the type of margin received against non-cleared OTC...

Figure 7.11 Illustration of a haircut applied to collateral.

Figure 7.12 Illustration of the methodology for estimating a haircut.

Figure 7.13 Illustration of the impact of margin on exposure without initial...

Figure 7.14 Illustration of the impact of margin on exposure, including init...

Figure 7.15 Illustration of the amount of margin for non-cleared OTC derivat...

Figure 7.16 Example of the impact of derivatives margin on other creditors (...

Figure 7.17 Illustration of the role of the MPoR.

Figure 7.18 Schematic illustration of the MPoR in bilateral markets.

Figure 7.19 Illustration of the increasing impact of margin on counterparty ...

Chapter 8

Figure 8.1 Illustration of direct clearing.

Figure 8.2 Illustration of complete clearing. The CCP assumes all contractua...

Figure 8.3 Illustration of bilateral markets (left) compared to centrally-cl...

Figure 8.4 Illustration of a centrally-cleared market including bilateral tr...

Figure 8.5 Illustration of multilateral offsetting afforded by central clear...

Figure 8.6 Illustration of SwapClear compression.

5

Figure 8.7 Illustration of the client clearing set-up where a client (C) acc...

Figure 8.8 Illustration of the margin period of risk (MPoR) for a CCP.

Figure 8.9 Illustration of a typical loss waterfall defining the way in whic...

Figure 8.10 Representation of the relationship between initial margin and de...

Figure 8.11 Comparison of different choices of initial margin and default fu...

Chapter 9

Figure 9.1 Illustration of risk factor shifts applied for determining the in...

Figure 9.2 Variation for S&P future and option contracts according to the da...

Figure 9.3 A combined move of total portfolio position in down and up volati...

Figure 9.4 Gains and losses for a portfolio consisting of a short equity ind...

Figure 9.5 Evolution of initial margin for an interest rate swap calculated ...

Figure 9.6 Illustration of historical simulation for an interest rate proces...

Figure 9.7 Evolution of initial margin (99% VAR) for an interest rate swap c...

Figure 9.8 Evolution of initial margin for an interest rate swap calculated ...

Figure 9.9 Illustration of procyclical and non-procyclical initial margin ca...

Figure 9.10 Evolution of initial margin (99% VAR) for an interest rate swap ...

Figure 9.11 Illustration of the impact of bilateral initial margin. The part...

Figure 9.12 Illustration of a variance-covariance approach to approximate th...

Figure 9.13 Illustration of delta and delta-gamma approximations compared to...

Chapter 10

Figure 10.1 Illustration of the loss waterfall and potential risk in the eve...

Figure 10.2 Illustration of tranching of default fund losses via auction inc...

Figure 10.3 Illustration of VMGH. The diagram on the left-hand side depicts ...

Figure 10.4 Illustration of partial tear-up. The diagram on the left-hand si...

Figure 10.5 Illustration of a potential feedback loop involving margin posti...

Figure 10.6 Comparison of loss allocation in bilateral (no margins), bilater...

Chapter 11

Figure 11.1 Illustration of the impact of a positive or negative contract va...

Figure 11.2 Illustration of potential future exposure. The grey area represe...

Figure 11.3 Illustration of exposure metrics for a single time horizon. PFE ...

Figure 11.4 Illustration of average EPE, which is the weighted average (the ...

Figure 11.5 Illustration of a square-root-of-time exposure profile. This exa...

Figure 11.6 Illustration of the exposure of swaps of different maturities. T...

Figure 11.7 Illustration of the cash flows of swap transactions of different...

Figure 11.8 Illustration of the exposure for swaps with equal and unequal pa...

Figure 11.9 Illustration of the cash flows in a swap transaction with differ...

Figure 11.10 Illustration of the floating cash flows (dotted lines) against ...

Figure 11.11 Illustration of the EFV, EPE, and ENE for a receiver interest r...

Figure 11.12 Illustration of the EFV, EPE, and ENE for a cross-currency swap...

Figure 11.13 Illustration of the EFV, EPE, and ENE for an ITM receiver inter...

Figure 11.14 Illustration of the EPE of a cross-currency swap (CCS) profile ...

Figure 11.15 Illustration of the exposure for cross-currency swaps of differ...

Figure 11.16 Exposure (PFE) for a swap-settled (physically-settled) interest...

Figure 11.17 Illustration of exercise of a physically-settled European swapt...

Figure 11.18 EPE and 99% PFE for a long-protection single-name CDS transacti...

Figure 11.19 Illustration of the impact of aggregation on exposure.

Figure 11.20 Schematic illustration of the impact of a negative future value...

Figure 11.21 Schematic illustration of the impact of a positive future value...

Figure 11.22 Illustration of the impact of margin on (positive) exposure, sh...

Figure 11.23 Illustration of the EPE of an interest rate swap with different...

Figure 11.24 Illustration of the impact of a positive or negative value and ...

Chapter 12

Figure 12.1 Illustration of the difference between real-world and risk-neutr...

Figure 12.2 Three different shapes of credit curve, all with a five-year spr...

Figure 12.3 Cumulative default probabilities for flat, upwards-sloping, and ...

Figure 12.4 Annual default probabilities for flat, upwards-sloping, and inve...

Figure 12.5 Schematic illustration of recovery settlement after a credit eve...

Figure 12.6 Illustration of classification of counterparties according to gl...

Figure 12.7 Example decision tree in order to map a given counterparty credi...

Figure 12.8 Illustration of a generic curve construction procedure. The cros...

Figure 12.9 Market practice for marking non-tradable credit curves.

Figure 12.10 Granularity of intersectional CDS data for the financial servic...

Figure 12.11 Illustration of defining a curve shape based on the shape of th...

Chapter 13

Figure 13.1 Evolution of regulatory methodologies with approximate timescale...

Figure 13.2 Approach to credit risk capital charge for counterparty credit r...

Figure 13.3 Illustration of advanced CVA capital methodology.

Figure 13.4 Example CVA capital charges for an uncollateralised and collater...

Figure 13.5 Illustration of the CEM approach to defining exposure at default...

Figure 13.6 Illustration of the SA-CCR multiplier that reduces the PFE when ...

Figure 13.7 Illustration of the use of IMM-calculated effective expected pos...

Figure 13.8 Illustration of effective EE (EEE) and effective EPE (EEPE).

Figure 13.9 Illustration of backtesting via comparing a realised path, at so...

Figure 13.10 EADs for uncollateralised (left) and collateralised (right) 10-...

Figure 13.11 EAD for an uncollateralised 10-year USD off-market interest rat...

Figure 13.12 EAD for two offsetting interest rate swaps in the same currency...

Figure 13.13 Capital calculations using different methodology choices for an...

Figure 13.14 Capital calculations using different methodology choices for an...

Figure 13.15 Implicit multiplier term in the standardised CVA capital charge...

Figure 13.16 Split of the implicit multiplier term in the standardised CVA c...

Figure 13.17 Impact of single-name CDS hedges on CVA capital under the stand...

Figure 13.18 Impact of index CDS hedges on CVA capital under the standardise...

Figure 13.19 SA-CVA capital charge for interest rate delta risk class of an ...

Figure 13.20 SA-CVA capital charge for the counterparty credit spread delta ...

Chapter 14

Figure 14.1 Simple illustration of funding and capital costs and their relat...

Figure 14.2 Simple illustration of charging capital requirements to originat...

Figure 14.3 Simple illustration of charging and remunerating funding require...

Figure 14.4 Market practice on pricing funding.

Figure 14.5 Market practice on pricing FVA into trades.

Figure 14.6 Illustration of the relationship between bilateral CVA (CVA and ...

Figure 14.7 Illustration of the funding cost for a bank.

Figure 14.8 Illustration of the historical relationship in US dollars betwee...

Figure 14.9 Illustration of cost of funding in different currencies and the ...

Chapter 15

Figure 15.1 Illustration of interest rate swap EPE as defined by swaption va...

Figure 15.2 Illustration of the EPE for a payer interest rate swap as define...

Figure 15.3 EPE, ENE, and EFV for an ITM portfolio.

Figure 15.4 A simple example of two different normal distributions with simi...

Figure 15.5 Marginal EPEs for the simple two-transaction example shown in Fi...

Figure 15.6 Illustration of the difference between path-wise and direct simu...

Figure 15.7 Illustration of time grid for exposure simulation.

Figure 15.8 PFE for a counterparty calculated at different levels of granula...

Figure 15.9 Illustration of cash flow bucketing in a single currency. The ca...

Figure 15.10 Illustration of the use of a proportion shift to correct an exp...

Figure 15.11 Illustration of the PFE for a five-year interest rate swap comp...

Figure 15.12 Illustration of the PFE for a 10-year cross-currency swap compu...

Figure 15.13 Illustration of the PFE for a 10-year cross-currency swap compu...

Figure 15.14 Illustration of the different requirements from scenario models...

Figure 15.15 Illustration of the portfolio hierarchy for xVA calculations wh...

Figure 15.16 Model versus actual implied volatility for swaptions in a HW1F ...

Figure 15.17 Schematic illustration of the impact of collateralisation on fu...

Figure 15.18 Schematic illustration of the use of MPoR to model the impact o...

Figure 15.19 Illustration of time grid for exposure simulation, with additio...

Figure 15.20 Incorporation of initial margin into IMM capital approaches. So...

Figure 15.21 Interest rate curve and forward values of co-terminal forward s...

Figure 15.22 Interest rate paths with the forward rates shown (solid line)....

Figure 15.23 Future values of the swap. The PFEs (5% and 95%) are shown by t...

Figure 15.24 EPE, ENE, and EFV of the swap from Monte Carlo simulation. Also...

Figure 15.25 EPE, ENE, and EFV for (top to bottom) a swap with unequal cash ...

Figure 15.26 EPE for a 20-year swap with a fixed rate equal to the 10Yx10Y f...

Figure 15.27 EPE, ENE, and PFE profiles for the 7Y payer IRS (top left), 5Yx...

Figure 15.28 Standalone and incremental exposures for the case of a directio...

Figure 15.29 Standalone and incremental exposures for the case of a risk-red...

Figure 15.30 Illustration of the breakdown of the EPE of the interest rate a...

Figure 15.31 Illustration of the standalone (top) and marginal (bottom) EPE ...

Figure 15.32 Exposure of standard and notional resetting cross-currency swap...

Figure 15.33 Illustration of an individual simulation path and the impact of...

Figure 15.34 Illustration of EPE (top) and 95% PFE (bottom) calculated with ...

Figure 15.35 Illustration of EPE calculated with different threshold assumpt...

Figure 15.36 EPE with and without IM.

Chapter 16

Figure 16.1 Illustration of the concept of ‘collateral discounting’.

Figure 16.2 Illustration of PCB and NCB for a fully-collateralised interest ...

Figure 16.3 Illustration of the collateral balance terms and EFV for the por...

Figure 16.4 Construction of a CTD curve.

Figure 16.5 CTD basis implied from Figure 16.4 using currency 1 as the base ...

Figure 16.6 ECB for a swap under a two-way and one-way margin agreement.

Figure 16.7 Market practice around the discounting curve used for collateral...

Chapter 17

Figure 17.1 Illustration of the complexity when calculating the CVA on a der...

Figure 17.2 Illustration of a direct CVA calculation.

Figure 17.3 Illustration of CVA formula. The component shown is the CVA cont...

Figure 17.4 The estimate of CVA for a 10-year receiver swap with path-wise a...

Figure 17.5 The estimate of CVA for a 10-year interest rate swap with path-w...

Figure 17.6 Correlation between valuations at successive points (two years, ...

Figure 17.7 CVA for payer and receiver interest rate swaps as a function of ...

Figure 17.8 CVA for 10-year receiver swap as the credit spread curve is incr...

Figure 17.9 CVA as a function of the LGD used when

Figure 17.10 CVA as a function of the LGD used for equal (

) and unequal (

...

Figure 17.11 Market practice around including DVA in pricing.

Figure 17.12 Incremental CVA (as a spread in bps per annum) for the balanced...

Figure 17.13 Incremental CVA (as a spread in bps per annum) for the balanced...

Figure 17.14 Impact of the initial margin and threshold (negative values) on...

Figure 17.15 Illustration of wrong-way and right-way risk exposure profiles ...

Figure 17.16 Illustration of exposure under the assumption of WWR for differ...

Figure 17.17 Future values of the swap with 90% (top) and -90% (bottom) corr...

Figure 17.18 Illustration of the structural approach to modelling general WW...

Figure 17.19 EPE of a payer interest rate swap calculated with WWR using int...

Figure 17.20 CVA as a function of the correlation between counterparty defau...

Figure 17.21 The Japan sovereign quanto basis for the dollar–yen pair.

Figure 17.22 Illustration of the currency jump approach to WWR for FX produc...

Figure 17.23 Fair CDS premium when buying protection subject to counterparty...

Figure 17.24 Comparison between a CCP loss waterfall and a CDO structure.

Chapter 18

Figure 18.1 Illustration of the source of funding costs (and benefits) withi...

Figure 18.2 (Top) Illustration of the funding needs on a payer interest rate...

Figure 18.3 Market practice around including survival probabilities in FVA c...

Figure 18.4 Illustration of equivalence between discounting at own cost of f...

Figure 18.5 Market practice for valuing uncollateralised transactions.

Figure 18.6 Illustration of the link between FBA and DVA.

Figure 18.7 Market practice on pricing CVA, DVA, and funding.

Figure 18.8 Upfront FCA and FBA for a receive fixed interest rate swap as a ...

Figure 18.9 Market practice on determining funding costs for FCA valuation a...

Figure 18.10 Illustration of the impact of asymmetric funding assumptions. T...

Figure 18.11 Possible funding profiles.

Figure 18.12 EFV, EPE, and ENE for the portfolio used for the example in Tab...

Figure 18.13 EFV (top) and EPE and ENE (bottom) profiles for the portfolio a...

Figure 18.14 EFV (top) and EPE and ENE (bottom) profiles for a risk-reducing...

Chapter 19

Figure 19.1 Qualitative example of the approach to capturing regulatory capi...

Figure 19.2 Total credit risk capital charge through time for a 10-year inte...

Figure 19.3 Simulations showing the evolution of counterparty risk capital f...

Figure 19.4 Expected capital profile (ECP) from Figure 19.3 broken down into...

Figure 19.5 Incremental EPE (top) and ECP (bottom) profiles for the 10-year ...

Figure 19.6 Expected exposure (EPE) (top) and projected capital charge (bott...

Figure 19.7 Illustration of ECP profile using traditional regulatory capital...

Figure 19.8 Illustration of CVA/FVA and KVA charges at entry and exit of a t...

Figure 19.9 Market view of the most significant causes of divergence in mark...

Figure 19.10 Simple illustration of the funding of a balance sheet with debt...

Figure 19.11 Exposure (top) and capital (bottom) profiles for the 1,000 noti...

Figure 19.12 Evolution of KVA in the three scenarios shown in Figure 19.11....

Figure 19.13 Annual ROC in the three scenarios shown in Figure 19.11.

Figure 19.14 ECP for the example shown in Section 19.2.4, assuming that KVA ...

Figure 19.15 Comparison of CVA and KVA for partial hedging scenarios.

Chapter 20

Figure 20.1 Market practice around pricing contingent funding requirements....

Figure 20.2 Forward IM for the balanced and directional interest rate swap p...

Figure 20.3 Distribution of future IM quantified by EIM and high and low qua...

Figure 20.4 Distribution of future IM quantified by EIM and high and low qua...

Figure 20.5 Distribution of future IM quantified by EIM and high and low qua...

Figure 20.6 Incremental EIM profiles for the five-year swap in the portfolio...

Figure 20.7 Illustration of MVA with both contingent and non-contingent comp...

Figure 20.8 Illustration of the origin of the CCP basis where a party trades...

Figure 20.9 Illustration of the origin of the CCP basis where a party trades...

Figure 20.10 KVA and MVA in bps upfront for a 10-year interest rate swap, as...

Figure 20.11 As in Figure 20.10, but with a cost of capital of 15% and a fun...

Chapter 21

Figure 21.1 Illustration of xVA hedging.

Figure 21.2 CVA credit spread sensitivity (parallel CS01) as a function of d...

Figure 21.3 Market practice on hedging of CVA Greeks.

Figure 21.4 JTD P&L as a function of the positive shift in the credit curve ...

Figure 21.5 Potential hedging benefit with a credit proxy, depending on corr...

Figure 21.6 Market practice on CVA limits.

Figure 21.7 Hedging performance for xVA desk (CVA and FVA), showing behaviou...

Figure 21.8 Overall ROC when using index CDS to hedge CVA capital.

Figure 21.9 Illustration of the impact of eligible and non-eligible xVA hedg...

Figure 21.10 P&L for KVA hedges in the three scenarios shown in Figure 19.11...

Figure 21.11 Worst-case (99% quantile) quarterly outflow for a two-way margi...

Guide

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For other titles in the Wiley Finance Series

please see www.wiley.com/finance

The xVA Challenge

Counterparty Risk, Funding, Collateral, Capital and Initial Margin

Fourth Edition

Jon Gregory

This edition first published 2020

© 2020 John Wiley & Sons, Ltd

First edition published 2009, second edition published 2012 by John Wiley & Sons, Ltd, third edition published 2015 by John Wiley and Sons, Ltd.

Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, United Kingdom

For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

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Library of Congress Cataloging-in-Publication Data

Names: Gregory, Jon, 1971- author.

Title: The xVA challenge : counterparty risk, funding, collateral, capital and initial margin / Jon Gregory.

Other titles: Counterparty credit risk and credit value adjustment Description: Fourth edition. | Chichester, West Sussex, United Kingdom :

John Wiley & Sons, 2020. | Includes bibliographical references and index.

Identifiers: LCCN 2019058762 (print) | LCCN 2019058763 (ebook) | ISBN 9781119508977 (hardback) | ISBN 9781119509028 (adobe pdf) | ISBN 9781119509004 (epub)

Subjects: LCSH: Derivative securities—Mathematical models. | Risk management.

Classification: LCC HG6024.A3 G74 2020 (print) | LCC HG6024.A3 (ebook) | DDC 332.64/57—dc23

LC record available at https://lccn.loc.gov/2019058762

LC ebook record available at https://lccn.loc.gov/2019058763

Cover Design: WileyCover Image: © Sandipkumar Patel/Getty Images

To Ginnie, George, Christy, Flo and Luna

List of Spreadsheets

One of the key features of the first and second editions of this book was the accompanying spreadsheets that were prepared to allow the reader to gain some simple insight into some of the quantitative aspects discussed. Many of these examples have been used for training courses and have therefore evolved to be quite intuitive and user-friendly. The spreadsheets can be downloaded freely from Jon Gregory's website, www.cvacentral.com, under the counterparty risk section. New examples may be added over time.

Spreadsheet 4.1  LCR example.

Spreadsheet 4.2  NSFR example.

Spreadsheet 6.1  Compression example.

Spreadsheet 7.1  Margin calculation including thresholds and initial margins.

Spreadsheet 9.1  Initial margin calculation of an interest rate swap using historical simulation.

Spreadsheet 9.2  Example ISDA SIMM™ calculations.

Spreadsheet 10.1  Illustration of Auction Incentive Pool (AIP) calculation.

Spreadsheet 10.2  Illustration of variation margin gains haircutting (VMGH) and selective tear-up approaches to loss allocation.

Spreadsheet 11.1  Simple exposure metric calculation.

Spreadsheet 11.2  EPE and PFE for a normal distribution.

Spreadsheet 11.3  Simple example of a cross-currency swap profile.

Spreadsheet 11.4  Simple calculation of the exposure of a CDS.

Spreadsheet 11.5  Simple two transaction example of netting effects.

Spreadsheet 11.6  Impact of variation and initial margin on exposure and funding.

Spreadsheet 12.1  Calculating risk-neutral default probabilities.

Spreadsheet 12.2  Example cross-sectional methodology for credit spreads.

Spreadsheet 13.1  Implementation of SA-CCR.

Spreadsheet 13.2  Calculation of ‘alpha’ factor.

Spreadsheet 13.3  EPE and EEPE example.

Spreadsheet 13.4  Comparison of capital costs across different methodologies.

Spreadsheet 15.1  Semianalytical calculation of the exposure for a swap.

Spreadsheet 15.2  Example marginal exposure calculation.

Spreadsheet 15.3  Simple simulation of an interest rate swap exposure.

Spreadsheet 15.4  Simple margin simulation based on portfolio value.

Spreadsheet 15.5  One-factor Hull-White model for exposure for interest rate products.

Spreadsheet 15.6  Illustration of the impact of netting.

Spreadsheet 15.7  Marginal EPEs.

Spreadsheet 15.8  Notional resetting cross-currency swap.

Spreadsheet 15.9  Quantifying the impact of margin on exposure.

Spreadsheet 16.1  ColVA calculation.

Spreadsheet 17.1  Direct CVA calculation for an interest rate swap.

Spreadsheet 17.2  Path-wise CVA calculation for an interest rate swap.

Spreadsheet 17.3  CVA and DVA calculations.

Spreadsheet 17.4  Incremental CVA and DVA calculations.

Spreadsheet 17.5  Marginal CVA and DVA calculations.

Spreadsheet 17.6  Simple wrong-way risk example.

Spreadsheet 17.7  Direct simulation of wrong-way risk for an interest rate swap.

Spreadsheet 17.8  Exposure distribution using a Gaussian copula approach.

Spreadsheet 18.1  Symmetric FVA calculation compared to discounting approach.

Spreadsheet 18.2  Asymmetric FVA calculation.

Spreadsheet 18.3  FVA Allocation.

Spreadsheet 19.1  KVA calculation for interest rate swap.

List of Appendices

The following is a list of Appendices that contain additional mathematical detail. These Appendices can be downloaded freely from www.cvacentral.com.

Appendix 7A Exposure and time period scaling

Appendix 11A Exposure metrics for a normal distribution

Appendix 11B Forward and swap exposure profiles

Appendix 11C Approximate cross-currency profile

Appendix 11D Simple aggregation example for a normal distribution

Appendix 12A Risk-neutral default probability calculation

Appendix 13A Large homogenous pool approximation for credit losses

Appendix 13B Standardised CVA capital formula

Appendix 15A Swaption analogy and the EPE of an interest rate swap

Appendix 15B Marginal EPE

Appendix 15C Collateralised EPE approx.

Appendix 15D Simple initial margin calculation

Appendix 16A ColVA formula

Appendix 17A CVA formula derivation

Appendix 17B CVA as a running spread

Appendix 17C CVA approx. via EPE

Appendix 17D Bilateral CVA formula (CVA and DVA)

Appendix 17E Incremental CVA

Appendix 17F Wrong-way risk and CVA

Appendix 17G CVA for a CDS contract

Appendix 18A FVA formula and discounting

Appendix 19A KVA calculation

Appendix 21A Beta hedging

Acknowledgements

The first edition of this book was published about a decade ago in the aftermath of a global financial crisis and focused on the importance of counterparty credit. Since then, the area of counterparty credit risk has broadened to consider the importance of related aspects such as collateral, funding, capital, and initial margin. This area has continued to see rapid change due to regulation, accounting standards, and evolving market practice. As previously, this is much more than a new edition because most of the content has been rewritten and expanded significantly.

I hope this book can be used as a comprehensive and relatively non-mathematical reference for the subject we now generally refer to as xVA. There are other mathematical books on this subject and the book by Andrew Green (Green 2015) is recommended as a comprehensive quantitative guide to the subject.

As with previous editions, I have saved space by putting mathematical appendices together with accompanying spreadsheets on my personal website at www.cvacentral.com. Since many do not study this material in depth, this has proved to be a reasonable compromise for most readers. There is also a list of errata that can be found on this website.

I have also made use of numerous survey results and I am grateful to Solum Financial and Deloitte for allowing me to reproduce these. I am also grateful to IBM and IHS Markit who have provided calculation examples in previous editions, some of which are used here. These will all be mentioned in the text.

Finally, I would like to thank the following people for feedback on this and earlier editions of the book: Manuel Ballester, Teimuraz Barbakadze, Ronnie Barnes, Raymond Cheng, Vladimir Cheremisin, Michael Clayton, Andrew Cooke, Christian Crispoldi, Daniel Dickler, Wei-Ming Feng, Julia Fernald, Leonard Fichte, Piero Foscari, Teddy Fredaigues, Sayoko Fujisawa, Naoyuki Fujita, Shota Fukamizu, Dimitrios Giannoulis, Glen Gibson, Sergej Goriatchev, Arthur Guerin, Kazuhisa Hirota, Kale Kakhiani, Toshiyuki Kitano, Henry Kwon, Edvin Lundstrom, David Mengle, Richard Morrin, Ivan Pomarico, Yufi Pak, Hans-Werner Pfaff, Francesco Ivan Pomarico, Erik van Raaij, Kei Sagami, Guilherme Sanches, Neil Schofield, Andreas Schwaderlapp, Florent Serre, Masum Shaikh, Ana Sousa, Salvatore Stefanelli, Richard Stratford, Carlos Sterling, Norikazu Takei, Hidetoshi Tanimura, Todd Tauzer, Satoshi Terakado, Nick Vause, Frederic Vrins, Nana Yamada, and Valter Yoshida.

Jon GregoryDecember 2019

About the Author

Jon Gregory is an independent expert specialising in counterparty risk and xVA related projects. He has worked on many aspects of credit risk and derivatives in his career, being previously with Barclays Capital, BNP Paribas, and Citigroup. He is a senior advisor for Solum Financial Derivatives Advisory. He is also a faculty member for London Financial Studies and the Certificate of Quantitative Finance. He currently serves on the Academic Advisory Board of IHS Markit and is a Managing Editor of the journal Quantitative Finance.

Jon has a PhD from Cambridge University.

Section 1Basics

1Introduction

In 2007, a global financial crisis (GFC) started which eventually became more severe and long-lasting than could have ever been anticipated. Along the way, there were major casualties such as the bankruptcy of the investment bank Lehman Brothers. Governments around the world had to bailout other financial institutions such as American International Group (AIG) in the US and the Royal Bank of Scotland in the UK.

The GFC caused a major focus on counterparty credit risk (CCR) which is the credit risk in relation to derivative products. A derivative trade is a contractual relationship that may be in force from a few days to several decades. During the lifetime of the contract, the two counterparties have claims against each other such as in the form of cash flows that evolve as a function of underlying assets and market conditions. Derivatives transactions create CCR due to the risk of insolvency of one party. This CCR in turn creates systemic risk due to derivatives trading volume being dominated by a relatively small number of large derivatives counterparties (‘dealers’) that are then key nodes of the financial system.

Post-GFC, participants in the derivatives market became more aware of CCR and its quantification via credit value adjustment (CVA). They also started to create more value adjustments, or xVAs, in order to quantify other costs such as funding, collateral, and capital. Derivatives pricing used to be focused on so-called ‘exotics’ with the majority of simple or vanilla derivatives thought to be relatively straightforward to deal with. However, the birth of xVA has changed this and even the most simple derivatives may have complex pricing and valuation issues arising from xVA.

Regulation has also enhanced the need to consider xVA (or XVA). Increasing capital requirements, constraints on funding, liquidity, and leverage together with a clearing mandate and bilateral margin requirements all make derivatives trading more expensive and complex. However, derivatives are still fundamentally important: for example, without them end users would have to use less effective hedges, which would create income statement volatility. The International Swaps and Derivatives Association (ISDA 2014b) reports that 85% of end users said that derivatives were very important or important to their risk management strategy and 79% said they planned to increase or maintain their use of over-the-counter (OTC) derivatives.

This book aims to fully explain xVA and the associated landscape of derivatives trading. Chapters 2 to 5 will discuss the basics of derivatives, regulation, CCR, and introduce the concept of xVA. Chapters 6 to 10 will discuss risk mitigation methods such as netting, margining, and central clearing. Chapters 11 to 15 will cover the building blocks of xVA such as exposure, credit spreads, funding, and capital costs. Finally, Chapters 16 to 20 will define the xVAs in sequence whilst also discussing their relationships to one another. Chapter 21 will discuss the ‘xVA desk’ and management of xVA.

The online Appendices and Spreadsheets provide more detail on various xVA calculations. This book is a relatively non-mathematical treatment of xVA. For a more mathematically-rigorous text for quantitative researchers, Andrew Green's book (Green 2015) is strongly recommended.

2Derivatives

2.1 INTRODUCTION

Derivatives transactions represent contractual agreements either to make payments or to buy or sell an underlying security at a time or times in the future. The times may range from a few weeks or months (for example, futures contracts) to many years (for example, long-dated swaps). The value of a derivative will change with the level of one or more underlying assets or indices and possibly decisions made by the parties to the contract. In many cases, the initial value of a traded derivative will be contractually configured to be zero for both parties at inception.

Derivatives are not a particularly new financial innovation; for example, in medieval times, forward contracts were popular in Europe. However, derivatives products and markets have become particularly large and complex in the last three decades. One of the advantages of derivatives is that they can provide very efficient hedging tools. For example, consider the following risks that an institution, such as a corporate, may experience:

Interest rate risk

. They need to manage liabilities such as transforming floating- into fixed-rate debt via an interest rate swap.

Foreign exchange (FX) risk

. Due to being paid in various currencies, there is a need to hedge cash inflow in these currencies, for example, using FX forwards.

Commodity risk

. The need to lock in commodity prices either due to consumption (e.g. airline fuel costs) or production (e.g. a mining company) via commodity futures or swaps.

In many ways, derivatives are no different from the underlying cash instruments. They simply allow one to take a very similar position in a synthetic way. For example, an airline wanting to reduce its exposure to a potential rise in oil price can buy oil futures, which are cash-settled and therefore represent a very simple way to go ‘long oil’ (with no storage or transport costs). An institution wanting to reduce its exposure to a certain asset can do so via a derivative contract (such as a total return swap), which means it does not have to sell the asset directly in the market.

There are many different users of derivatives such as sovereigns, central banks, regional/local authorities, hedge funds, asset managers, pension funds, insurance companies, and non-financial corporations. All use derivatives as part of their investment strategy or to hedge the risks they face from their business activities. Due to the particular hedging needs of institutions and related issues, such as accounting, many derivatives are relatively bespoke. For example, a corporation wanting to hedge the interest rate risk in a floating-rate loan will want an interest rate swap precisely matching the terms of the loan (e.g. maturity, payment frequency, and reference rate).

Financial institutions, mainly banks, provide derivative contracts to their end user clients and hedge their risks with one another. Whilst many financial institutions trade derivatives, many markets are dominated by a relatively small number of large counterparties (often known as ‘dealers’). Such dealers represent key nodes of the financial system. For example, there are currently around 35 globally-systemically-important banks (G-SIBs), which is a term loosely synonymous with ‘too big to fail’. G-SIB banks are subject to stricter rules, such as higher minimum capital requirements.

During the lifetime of a derivatives contract, the two counterparties have claims against each other, such as in the form of cash flows that evolve as a function of underlying assets and market conditions. Derivatives transactions create counterparty credit risk (counterparty risk) due to the risk of insolvency of one party. Counterparty risk refers to the possibility that a counterparty may not meet its contractual requirements under the contract when they become due.

Counterparty risk is managed over time through clearing; this can be performed bilaterally, where each counterparty manages the risk of the other, or centrally through a central counterparty (CCP). As the derivatives market has grown, so has the importance of counterparty risk. Furthermore, the lessons from events such as the bankruptcy of Lehman Brothers have highlighted the problems when a major player in the derivatives market defaults. This, in turn, has led to an increased focus on counterparty risk and related aspects.

2.2 THE DERIVATIVES MARKET

2.2.1 Exchange-traded and OTC Derivatives

Within the derivatives markets, many of the simplest products are traded through exchanges. A derivatives exchange is a financial centre (Figure 2.1) where parties can trade standardised contracts such as futures and options at a specified price. An exchange promotes market efficiency and enhances liquidity by centralising trading in a single place, thereby making it easier to enter and exit positions. Exchange-traded derivatives are standardised contracts (e.g. futures and options) and are actively traded. It is easy to buy a contract and sell the equivalent contract to terminate (‘close’) the position, which can be done via one or more derivative exchanges. Prices are transparent and accessible to a wide range of market participants.

Figure 2.1 Illustration of exchange-traded and bilaterally-traded derivatives.