XVA E-Book

Andrew Green

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

Seitenzahl: 939

Veröffentlichungsjahr: 2015

Beschreibung

Thorough, accessible coverage of the key issues in XVA

XVA – Credit, Funding and Capital Valuation Adjustments provides specialists and non-specialists alike with an up-to-date and comprehensive treatment of Credit, Debit, Funding, Capital and Margin Valuation Adjustment (CVA, DVA, FVA, KVA and MVA), including modelling frameworks as well as broader IT engineering challenges. Written by an industry expert, this book navigates you through the complexities of XVA, discussing in detail the very latest developments in valuation adjustments including the impact of regulatory capital and margin requirements arising from CCPs and bilateral initial margin.

The book presents a unified approach to modelling valuation adjustments including credit risk, funding and regulatory effects. The practical implementation of XVA models using Monte Carlo techniques is also central to the book. You'll also find thorough coverage of how XVA sensitivities can be accurately measured, the technological challenges presented by XVA, the use of grid computing on CPU and GPU platforms, the management of data, and how the regulatory framework introduced under Basel III presents massive implications for the finance industry.

• Explores how XVA models have developed in the aftermath of the credit crisis
• The only text to focus on the XVA adjustments rather than the broader topic of counterparty risk.
• Covers regulatory change since the credit crisis including Basel III and the impact regulation has had on the pricing of derivatives. 
• Covers the very latest valuation adjustments, KVA and MVA.
• The author is a regular speaker and trainer at industry events, including WBS training, Marcus Evans, ICBI, Infoline and RISK

If you're a quantitative analyst, trader, banking manager, risk manager, finance and audit professional, academic or student looking to expand your knowledge of XVA, this book has you covered.

Leseprobe

For other titles in the Wiley Finance series please see www.wiley.com/finance

XVA: Credit, Funding and Capital Valuation Adjustments

ANDREW GREEN

This edition first published 2016 © 2016 John Wiley & Sons Ltd

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Library of Congress Cataloging-in-Publication Data

Green, Andrew,    XVA : credit, funding and capital valuation adjustments / Andrew Green.       pages cm. — (The wiley finance series)    Includes bibliographical references and index.    ISBN 978-1-118-55678-8 (hardback) — ISBN 978-1-118-55675-7 (ebk) — ISBN 978-1-118-55676-4 (ebk) — ISBN 978-1-119-16123-3 (ebk)   1. Finance.    2. Derivative securities.   I. Title.    HG173.G744 2015    332.64′57–dc23

2015019353

A catalogue record for this book is available from the British Library.

ISBN 978-1-118-55678-8 (hardback)   ISBN 978-1-118-55675-7 (ebk) ISBN 978-1-118-55676-4 (ebk)          ISBN 978-1-119-16123-3 (obk)

Cover Design: Wiley

Cover Image: ©iStock/Tuomas Kujansuu

For Simone

Contents

Acknowledgements

CHAPTER 1 Introduction: The Valuation of Derivative Portfolios

1.1 What this book is about

1.2 Prices and Values

1.3 Trade Economics in Derivative Pricing

1.4 Post-Crisis Derivative Valuation or How I Learned to Stop Worrying and Love FVA

1.5 Reading this Book

Notes

PART ONE CVA and DVA: Counterparty Credit Risk and Credit Valuation Adjustment

CHAPTER 2 Introducing Counterparty Risk

2.1 Defining Counterparty Risk

2.2 CVA and DVA: Credit Valuation Adjustment and Debit Valuation Adjustment Defined

2.3 The Default Process

2.4 Credit Risk Mitigants

Notes

CHAPTER 3 CVA and DVA: Credit and Debit Valuation Adjustment Models

3.1 Introduction

3.2 Unilateral CVA Model

3.3 Bilateral CVA Model: CVA and DVA

3.4 Modelling Dependence between Counterparties

3.5 Components of a CVA Calculation Engine

3.6 Counterparty Level CVA vs. Trade Level CVA

3.7 Recovery Rate/Loss-Given-Default Assumptions

Notes

CHAPTER 4 CDS and Default Probabilities

4.1 Survival Probabilities and CVA

4.2 Historical versus Implied Survival Probabilities

4.3 Credit Default Swap Valuation

4.4 Bootstrapping the Survival Probability Function

4.5 CDS and Capital Relief

4.6 Liquid and Illiquid Counterparties

Notes

CHAPTER 5 Analytic Models for CVA and DVA

5.1 Analytic CVA Formulae

5.2 Interest Rate Swaps

5.3 Options: Interest Rate Caplets and Floorlets

5.4 FX Forwards

CHAPTER 6 Modelling Credit Mitigants

6.1 Credit Mitigants

6.2 Close-out Netting

6.3 Break Clauses

6.4 Variation Margin and CSA Agreements

6.5 Non-financial Security and the Default Waterfall

Notes

CHAPTER 7 Wrong-way and Right-way Risk for CVA

7.1 Introduction: Wrong-way and Right-way Risks

7.2 Distributional Models of Wrong-way/ Right-way Risk

7.3 A Generalised Discrete Approach to Wrong-Way Risk

7.4 Stochastic Credit Models of Wrong-way/Right-way Risk

7.5 Wrong-way/Right-way Risk and DVA

Notes

PART TWO FVA: Funding Valuation Adjustment

CHAPTER 8 The Discount Curve

8.1 Introduction

8.2 A Single Curve World

8.3 Curve Interpolation and Smooth Curves

8.4 Cross-currency Basis

8.5 Multi-curve and Tenor Basis

8.6 OIS and CSA Discounting

8.7 Conclusions: Discounting

Notes

CHAPTER 9 Funding Costs: Funding Valuation Adjustment (FVA)

9.1 Explaining Funding Costs

9.2 First Generation FVA: Discount Models

9.3 Double Counting and DVA

9.4 Second Generation FVA: Exposure Models

9.5 Residual FVA and CSAs

9.6 Asymmetry

9.7 Risk Neutrality, Capital and the Modigliani-Miller Theorem

9.8 Wrong-way/Right-way Risk and FVA

Notes

CHAPTER 10 Other Sources of Funding Costs: CCPs and MVA

10.1 Other Sources of Funding Costs

10.2 MVA: Margin Valuation Adjustment by Replication

10.3 Calculating MVA Efficiently

10.4 Conclusions on MVA

Notes

CHAPTER 11 The Funding Curve

11.1 Sources for the Funding Curve

11.2 Internal Funding Curves

11.3 External Funding Curves and Accounting

11.4 Multi-currency/Multi-asset Funding

PART THREE KVA: Capital Valuation Adjustment and Regulation

CHAPTER 12 Regulation: the Basel II and Basel III Frameworks

12.1 Introducing the Regulatory Capital Framework

12.2 Market Risk

12.3 Counterparty Credit Risk

12.4 CVA Capital

12.5 Other Sources of Regulatory Capital

12.6 Forthcoming Regulation with Pricing Impact

Notes

CHAPTER 13 KVA: Capital Valuation Adjustment

13.1 Introduction: Capital Costs in Pricing

13.2 Extending Semi-replication to Include Capital

13.3 The Cost of Capital

13.4 KVA for Market Risk, Counterparty Credit Risk and CVA Regulatory Capital

13.5 The Size of KVA

13.6 Conclusion: KVA

Notes

CHAPTER 14 CVA Risk Warehousing and Tax Valuation Adjustment (TVA)

14.1 Risk Warehousing XVA

14.2 Taxation

14.3 CVA Hedging and Regulatory Capital

14.4 Warehousing CVA Risk and Double Semi-Replication

CHAPTER 15 Portfolio KVA and the Leverage Ratio

15.1 The Need for a Portfolio Level Model

15.2 Portfolio Level Semi-replication

15.3 Capital Allocation

15.4 Cost of Capital to the Business

15.5 Portfolio KVA

15.6 Calculating Portfolio KVA by Regression

Notes

PART FOUR XVA Implementation

CHAPTER 16 Hybrid Monte Carlo Models for XVA: Building a Model for the Expected-Exposure Engine

16.1 Introduction

16.2 Choosing the Calibration: Historical versus Implied

16.3 The Choice of Interest Rate Modelling Framework

16.4 FX and Cross-currency Models

16.5 Inflation

16.6 Equities

16.7 Commodities

16.8 Credit

Notes

CHAPTER 17 Monte Carlo Implementation

17.1 Introduction

17.2 Errors in Monte Carlo

17.3 Random Numbers

17.4 Correlation

17.5 Path Generation

Notes

CHAPTER 18 Monte Carlo Variance Reduction and Performance Enhancements

18.1 Introduction

18.2 Classic Methods

18.3 Orthogonalisation

18.4 Portfolio Compression

18.5 Conclusion: Making it Go Faster!

CHAPTER 19 Valuation Models for Use with Monte Carlo Exposure Engines

19.1 Valuation Models

19.2 Implied Volatility Modelling

19.3 State Variable-based Valuation Techniques

Note

CHAPTER 20 Building the Technological Infrastructure

20.1 Introduction

20.2 System Components

20.3 Hardware

20.4 Software

20.5 Conclusion

Notes

PART FIVE Managing XVA

CHAPTER 21 Calculating XVA Sensitivities

21.1 XVA Sensitivities

21.2 Finite Difference Approximation

21.3 Pathwise Derivatives and Algorithmic Differentiation

21.4 Scenarios and Stress Tests

Notes

CHAPTER 22 Managing XVA

22.1 Introduction

22.2 Organisational Design

22.3 XVA, Treasury and Portfolio Management

22.4 Active XVA Management

22.5 Passive XVA Management

22.6 Internal Charging for XVA

22.7 Managing Default and Distress

PART SIX The Future

CHAPTER 23 The Future of Derivatives?

23.1 Reflecting on the Years of Change...

23.2 The Market in the Future

Bibliography

Index

EULA

List of Tables

Chapter 1

Table 1.1

Table 1.2

Chapter 2

Table 2.1

Chapter 3

Table 3.1

Table 3.2

Table 3.3

Chapter 4

Table 4.1

Table 4.2

Chapter 7

Table 7.1

Chapter 9

Table 9.1

Table 9.2

Table 9.3

Chapter 10

Table 10.1

Table 10.2

Chapter 12

Table 12.1

Table 12.2

Table 12.3

Table 12.4

Table 12.5

Table 12.6

Table 12.7

Table 12.8

Table 12.9

Table 12.10

Table 12.11

Table 12.12

Table 12.13

Table 12.14

Chapter 13

Table 13.1

Table 13.2

Table 13.3

Table 13.4

Table 13.5

Chapter 14

Table 14.1

Chapter 15

Table 15.1

Chapter 16

Table 16.1

Table 16.2

Table 16.3

Table 16.4

Chapter 17

Table 17.1

Chapter 20

Table 20.1

Table 20.2

Chapter 22

Table 22.1

Table 22.2

List of Illustrations

Chapter 1

Figure 1.1

The different calculation methodologies available for market risk, counterparty credit risk and CVA under the Basel III framework. The more complex methodologies requiring regulatory approval are lower down the figure.

Figure 1.2

A diagram of a price negotiation between two parties A and B. Both parties have a

most favoured price

that they would ideally like to transact at and a

walk way price

below which they will not trade. The agreed price must lie between the most favoured price and walk away price of both parties. If these ranges do not overlap then no agreement is possible.

Chapter 2

Figure 2.1

The expected positive and expected negative exposure profiles for a five-year interest rate swap with a notional of £100m at trade inception.

Figure 2.2

The impact of close-out netting reducing overall credit exposure.

Figure 2.3

The repo/reverse repo transaction flows.

Figure 2.4

A swap with and without a break clause and the associated expected positive exposure profile. For the swap with the break clause, the CVA is lower.

Chapter 3

Figure 3.1

The components of a CVA calculation engine.

Chapter 4

Figure 4.1

The cash flows of a credit default swap.

Figure 4.2

The hazard rate values for a piecewise constant hazard rate model of a credit curve.

Figure 4.3

The hazard rate values for a piecewise constant hazard rate model of a credit curve just prior to the CDS roll date and on the next business date after the roll. The CDS spreads were held constant at the values given in Table 4.1. The shift in the hazard rates and the date segments over which they are defined can be seen in the differences between the two curves.

Chapter 6

Figure 6.1

Two example loan packages with security. In case 1 the derivative ranks lower than the loan and in case 2 it ranks

pari passu

with the loan.

Chapter 7

Figure 7.1

The EPE and percentile profiles of a 30-year interest rate swap.

Figure 7.2

The unilateral CVA for a 30-year GBP interest rate swap using the bivariate Gaussian Copula model.

Figure 7.3

The unilateral CVA for a 30-year GBP interest rate swap using the Hull-White variant wrong-way risk model.

Chapter 8

Figure 8.1

The spread between 3-month EURIBOR and 3-month EONIA swap rate during the financial crisis period of 2007–2009. The spread started the period at only 6 basis points before peaking around 180 basis points and then falling below 30 basis points at the end of 2009. (Source: European Banking Federation)

Figure 8.2

Cash flows for an instantaneous FX swap. The solid lines are cash flows in the domestic currency and the dash lines are in the foreign currency.

Chapter 9

Figure 9.1

The exposure profile of an in-the-money interest rate swap.

Figure 9.2

The exposure profile of a loan with notional scaled to give the same MTM as the swap above.

Figure 9.3

The exposure profile of an out-of-the-money interest rate swap.

Figure 9.4

The exposure profile of a deposit with notional scaled to give the same MTM as the swap above.

Figure 9.5

The collateral flows associated with a client trade fully secured using a CSA and hedged in the market under an identical CSA. When the client trade has a positive mark-to-market to the bank it receives collateral from the client and immediately posts this to the hedge counterparty. When the client trade has a negative mark-to-market to the bank it posts collateral to the client but receives collateral from the hedge counterparty. Assuming both CSAs allow rehypothecation of collateral there is no additional funding requirement.

Figure 9.6

The collateral flows associated with an unsecured client trade that is hedged in the market under a CSA. When the client trade has a positive mark-to-market to the bank, the hedge trade has a negative mark-to-market and requires collateral. As there is no collateral available from the client, the bank borrows unsecured in the money markets. When the client trade has a negative mark-to-market to the bank it is not required to post collateral to the client but receives collateral from the hedge counterparty. The bank now has excess collateral that could be rehpothecated elsewhere.

Figure 9.7

Holding costs scenario 1. Two banks

A

and

B

have exactly the same trades with the same two counterparties, a clearing house and a client. The trades with the clearing house are fully collateralised, while the client trades are uncollateralised. The swap trades 1 and 2 are identical apart from the sign and the fixed rate and represent a client trade that has been hedged with a cleared trade.

Figure 9.8

Holding costs scenario 2. Like scenario 1, two banks

A

and

B

have exactly the same trades with the same two counterparties, a clearing house and a client. However, here bank

B

has a second client with an identical but opposite trade to the first client. To hedge this second transaction a second trade is cleared through the CCP, which offsets the first. As before, the trades with the clearing house are fully collateralised, while the client trades are uncollateralised.

Chapter 10

Figure 10.1

The collateral flows associated with a trade between a bank and a corporate and the associated hedge cleared through a CCP. The variation margin is met with rehypothecation of collateral; however, the initial margin, volatility buffer and default fund contributions must be posted irrespective of the mark-to-market of the trade. Given there is no rehypothecable source of collateral, the bank must borrow unsecured to fund the initial margin and this unsecured borrowing gives rise to FVA.

Chapter 16

Figure 16.1

UK CPI between January 2005 and December 2013 (Adapted from data from the Office for National Statistics licensed under the Open Government Licence v.2.0).

Figure 16.2

The effect of the length of window on measured historical correlation. The measured historical correlation between EURUSD and EURGBP spot between late 1999 and the end of 2009 is shown for four different choices of window; 25, 50, 100 and 200 days. The longer time series windows are considerably less volatile than the shorter ones.

Figure 16.3

Popular interest rate models and modelling frameworks and the relationships between them. Of course the number of different types of interest rate model is vast and only a subset is shown.

Figure 16.4

Forward rates in the log-normal forward rate market model. Forward rates are denoted by F, times by T and day-count fractions by τ.

Figure 16.5

The standard approach to a LFM model is to choose time steps equal to the durations of each of the forward rates. Then each forward evolves through a series of time steps until it fixes, giving the upper triangle arrangement illustrated here.

Chapter 17

Figure 17.1

The expected positive exposure profile for an interest rate swap with a semi-annual fixed leg and a quarterly floating leg. The expected positive exposure was calculated using four different Monte Carlo time step frequencies of 12, 6, 3 and 1 month. Only the quarterly and monthly simulation schedules resolve the features of the swap exposure profile.

Figure 17.2

Convergence of a CVA calculation using pseudo-random numbers from the Mersenne Twister. The test case was a GBP 10-year interest rate swap at par.

Figure 17.3

Two dimension projection of points from the Sobol sequence.

Figure 17.4

Two dimension projection of pseudo-random numbers.

Figure 17.5

Two dimension projection of points from the Sobol sequence.

Figure 17.6

Sobol points with Cranley-Patterson rotation.

Figure 17.7

Generating paths of Brownian motion by backward induction. The order in which the steps are taken is labelled by the numbers in the figure. The pattern aligns the lowest dimensions in the sequence with the largest steps in the Brownian motion and hence this approach is frequently used with quasi-random sequences to maximise the benefit that can be gained from the better properties of the lower dimensions.

Chapter 18

Figure 18.1

Convergence of the orthogonalisation scheme compared to plain pseudo-random numbers. The test case was a swap portfolio consisting of three 10-year interest rate swaps in GBP, EUR and USD, with all swaps at par. Five stochastic factors were used in the simulation for three interest rate processes and two FX processes. The unilateral CVA was then calculated and the standard error computed from 16 independent batches that when combined gave the listed path count.

Chapter 19

Figure 19.1

The grid interpolation valuation technique; the PDE grid is interpolated at the time steps of the Monte Carlo.

Chapter 20

Figure 20.1

XVA logical system workflow. The workflow for an XVA system can be split into three separate phases, input data preparation, calculation and reporting.

Figure 20.2

Typically individual trade records will be stored in the repositories of multiple different trading systems, each with their own proprietary data formats and databases. XVA needs to have access to all of the relevant trades. This will typically involve a common trade format and ideally a common trade access layer or “bus”.

Figure 20.3

A typical calibration hierarchy for an XVA Monte Carlo model.

Figure 20.4

Workflow for the counterparty or netting set orientated simulation.

Figure 20.5

Workflow for a global XVA simulation.

Figure 20.6

Workflow for Longstaff-Schwartz regression.

Figure 20.7

The steps in the waterfall model of software development (after Royce, 1970).

Figure 20.8

The Agile Manifesto.

Figure 20.9

A simplified flow graph describing the sub-tasks in an XVA calculation. The simulation has been divided up into four separate parallel tasks.

Chapter 21

Figure 21.1

The interaction between a tenor-based time partition and cash flows when calculating expected exposures is illustrated in the three diagrams, (a), (b) and (c). In case (a) the cash flow occurs one business day after the exposure date so that the expected exposure at

time step

includes the effect of the cash flow. In case (b) the cash flow occurs on the same business date as the time step and so will be included if the model includes

cash-on-the-day

in the trade valuation. Finally in case (c), one day further on, the tenor-based time step has rolled across the cash flow meaning it is no longer included and the exposure will drop.

Figure 21.2

The interaction between a tenor-based time partition and regular cash flows is illustrated in (a) and (b). Case (b) shows that the tenor-based schedule rolls across all the regular cash flows on the same date.

Figure 21.3

An example step-wise explain for a counterparty portfolio with interest rate and FX products.

Figure 21.4

An example of

differential exercise

occurring in an XVA Monte Carlo simulation. In case (a) the option exercises at the time step indicated into an interest swap giving value on this path at subsequent time steps. In case (b) interest rates have been shifted down, although as common random numbers have been used, the path retains the original shape. However, exercise no longer occurs and the option expires out of the money. Hence the later steps have no value. The results for the two paths are considerably different adding significant noise to the simulation.

Chapter 22

Figure 22.1

The organisational design with multiple independent XVA desks. When a new client trade is structured the sales team would potentially have to engage multiple XVA desks in addition to the appropriate derivative trading desk. The XVA functions may need to engage with each other to optimise the trade structure for XVA. A central XVA system would mitigate the complexity of interaction.

Figure 22.2

The organisational design with asset-class aligned XVA desks. This design can work as long as XVA calculation is centralised and allocated to the individual businesses.

Figure 22.3

The organisational design with a central XVA desk. This design means that new trades typically only involve a single derivative trading desk and the central XVA function. Note that here the client trade will appear in the trading book of the derivative trading business and only the XVA will appear in the trading book of the XVA desk.

Figure 22.4

In this design the central XVA desk faces the client directly so the full client trade is placed in the trading book of the XVA desk. The derivative trading desks then hedge out the risks on the trade including those of the XVA position.

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Acknowledgements

I would like to thank both Dr Chris Dennis and Dr Chris Kenyon for kindly agreeing to review this book prior to publication and for their work on a number of research topics that are contained within this book. Any errors or omissions are my own, however.

I would also like to thank the many colleagues and peers from both market and academia with whom I have had useful discussions on quantitative finance over many years. This includes colleagues from my current and past employers but also includes a great many others.

I owe a debt of gratitude to my many teachers over a number of years, but perhaps most of all to my DPhil supervisor, Professor James Binney, whose own publications inspired me ultimately to write my own book.

Finally I would like to thank friends and family for putting up with my absence during the writing process.

CHAPTER 1Introduction: The Valuation of Derivative Portfolios

Price is what you pay. Value is what you get.

—Warren Buffett American business magnate, investor and philanthropist (1930–)

1.1 What this book is about

This book is about XVA or Valuation Adjustments, the valuation of the credit, funding and regulatory capital requirements embedded in derivative contracts. It introduces Credit Valuation Adjustment (CVA) and Debit Valuation Adjustment (DVA) to account for credit risk, Funding Valuation Adjustment (FVA) for the impact of funding costs including Margin Valuation Adjustment (MVA) for the funding cost associated with initial margin, Capital Valuation Adjustment (KVA) for the impact of Regulatory Capital and Tax Valuation Adjustment (TVA) for the impact of taxation on profits and losses. The book provides detailed descriptions of models to calculate the valuation adjustments and the technical infrastructure required to calculate them efficiently. However, more fundamentally this book is about the valuation and pricing of derivative contracts. The reality is that credit, funding and capital concerns are very far from minor adjustments to the value of a single derivative contract or portfolio of derivatives. The treatment of CVA, DVA, FVA, MVA, KVA and TVA as adjustments reflects the historical development of derivative models and typical bank organisational design rather than the economic reality that places credit, funding and capital costs at the centre of accurate pricing and valuation of derivatives.