XVA

Credit, Funding and Capital Valuation Adjustments

Andrew Green

• Publisher: Wiley
• Year: 2015
• Print ISBN: 9781118556788
• eBook ISBN: 9781118556764
• Edition: 1
• Topic: Business
• Subtopic: Finance
• Index: Business

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.

CHAPTER 1
Introduction: 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.

Since the seminal papers by Fischer Black and Myron Scholes and Robert C. Merton published in 1973, derivative pricing and valuation has been centred in the Black-Scholes-Merton framework complete with its simplifying assumptions:

• Arbitrage opportunities do not exist.
• Any amount of money can be borrowed or lent at the risk-free rate which is constant and accrues continuously in time.
• Any amount of stock can be bought or sold including short selling with no restrictions.
• There are no transaction taxes or margin requirements.
• The underlying asset pays no dividend.
• The asset price is a continuous function with no jumps.
• The underlying asset has a constant volatility.
• Neither counterparty to the transaction is at risk of default.
• The market is complete, that is there are no unhedgeable risks.

It could also be argued that there are additional implicit assumptions underlying the Black-Scholes-Merton framework:

• No capital requirement or costs associated with regulatory requirements such as liquidity buffers
• No price impact of trading
• The Modigliani-Millar theorem on the separation of funding and investment decisions applies to derivatives (Modigliani and Miller, 1958).

However, even in the mid-1970s it was clear that these assumptions were there to simplify the problem of option pricing and were not a reflection of reality. Subsequently, a number of authors sought to relax these assumptions:

• Constant interest rates – Merton (1973)
• No dividends – Merton (1973)
• No transaction costs – Ingersoll (1976)
• Jumps – Merton (1976), Cox and Ross (1976).

Subsequently, the original formulation of Black-Scholes in terms of partial differential equations has been replaced by measure-theoretic probability through the work of Harrison and Kreps (1979), Harrison and Pliska (1983) and Geman, Karoui and Rochet (1995). The Black-Scholes model itself has been steadily adapted to match market prices such as through the use of market implied volatilities that display a skew or smile relative to the single flat volatility assumption of Black-Scholes, implicitly indicating that the stock price distribution has fatter tails than those implied by the log-normal distribution. Nevertheless, the essential framework of risk-neutral valuation through replication has remained largely unchanged even though the mathematical machinery used by quantitative analysts has been enhanced significantly and the computational power available to derivatives businesses has grown exponentially.

The survival of the model is best illustrated through belief in the law of one price. The law of one price can be stated as follows:

The same asset must trade at the same price on all markets (or there is an arbitrage opportunity).

This simple statement seems very persuasive at first glance. If an asset is quoted at price x on market X and at price y on market Y and x < y then asset buyers acting rationally should

1. buy assets from market X if they need to consume the asset
2. buy assets from market X and sell on market Y to make a riskless profit of (y − x),

that is, this market permits arbitrage.¹ However, in the context of derivatives it is not clear that the law of one price always applies:

• Over-the-counter (OTC) derivatives trade under bilateral agreements brokered under ISDA rules. The considerable variations in the terms of these legal rules mean that each ISDA (possibly coupled with a CSA) is effectively unique and hence so are the derivatives contracts traded between the two parties to the ISDA agreement.
• Counterparty risk is always present in practice because even under the strongest CSA terms there will still be delays between movements in portfolio mark-to-market valuations and calls/returns on collateral. Counterparty risk makes each derivative with a different counterparty unique with a distinct valuation. The traditional understanding of the law of one price no longer applies, as there are multiple derivatives with the same basic parameters with different prices. However, the law of one price could be preserved if we consider each pair of counterparties to be a different “market”, although this reduces the “law” to irrelevance. If both counterparties to a trade use a unilateral model of CVA, where only the risk of the counterparty defaulting is considered, neither party will agree on the value of the transaction so the value is asymmetric between the two counterparties. The introduction of bilateral models for counterparty risk and DVA allows symmetry of valuation to be restored,² but FVA models have again broken the symmetry. The introduction of KVA and the realisation that different institutions have different capital regimes has broken the symmetry irrevocably.
• Counterparties clearly have asymmetric access to markets.
• Many derivatives, particularly for large corporates, are transacted on an auction basis. This means that there is one agreed price with the derivative provider that the corporate ultimately selects. However, individual derivative dealers will have different values for the same underlying transaction.
• Once transacted many corporate derivatives are essentially illiquid. Novations of trades to third parties do occur, but infrequently. If the derivative dealer were to instigate a novation this might threaten the banking relationship. Smaller counterparties will typically have a limited number of banking relationships or perhaps only one banking relationship. Novations would likely prove impossible to do in such cases as with no established banking relationship it is unlikely other derivative providers would have sufficient information on the small counterparty to be able to provide the required credit limits. The deal could only be torn up by agreement with the relationship bank.
• Counterparties will often transact a derivative under completely different accounting regimes. For example, a corporate may hold a derivative under IRS 39 hedge accounting rules, while the bank counterparty may include the derivative in a trading book under mark-to-market accounting rules.

The only case where the law of one price might be said to hold is in the case of very liquid exchange-traded derivatives such as futures or exchange-traded options (ETOs). In such cases, given the derivative is entirely commoditised and that margin arrangements are equal for all market participants then the price can be said to be that of the last transaction that took place on the exchange. However, the law of one price has remained persistent in the world of quantitative finance.

The reality of the derivatives market in the aftermath of the default of Lehman brothers is very different from the idealised one encapsulated in the assumptions underlying the Black-Scholes model and risk-neutral valuation:

• Apparent arbitrage opportunities sometimes persist in the market. For example the Repurchase Overnight Index Average Rate (RONIA) is frequently higher than the Sterling Overnight Index Average Rate (SONIA) despite the fact RONIA relates to a secured lending market while SONIA relates to unsecured len...

Table of contents

• Cover
• Series
• Title page
• Copyright
• Dedication
• Acknowledgements
• CHAPTER 1 Introduction: The Valuation of Derivative Portfolios
• PART ONE CVA and DVA: Counterparty Credit Risk and Credit Valuation Adjustment
• PART TWO FVA: Funding Valuation Adjustment
• PART THREE KVA: Capital Valuation Adjustment and Regulation
• PART FOUR XVA Implementation
• PART FIVE Managing XVA
• PART SIX The Future
• Bibliography
• Index
• EULA