should be clear that:
What is a Derivative Valuation?
A valuation is a numerical measure of the worth of a contract. The law of one price suggests that there is just one valuation for a derivative; in reality this is not the case and different agents have different measures of worth in different contexts. Here I consider three valuations, but the list is not exhaustive:
• Accounting valuation
• Trading valuation
• Regulatory valuation.
There is nothing new here and bond traders, for example, have used the concept of relative value for many years. Before the crisis these different valuations generally coincided for unsecured derivatives as bank credit spreads were narrow and funding costs were negligible. The credit crisis drove the valuations apart and it is unlikely they will ever coincide again for unsecured derivatives. Valuation, even of simple products, has become a challenge.
Accounting valuations
Accounting valuations aim to provide an objective measure of the value of assets and liabilities on the balance sheet. Accounting valuation methodology is driven by
• Accounting standards (FSB, IFRS)
• Accounting principles (e.g. GAAP)
• Company law.
Sometimes these can be in conflict when market practice changes and it can take some time for these to be reflected back into accounting standards.
Trading valuations
These provide a valuation measure that reflects all of the risk factors that the derivative is currently understood to be subject to. The valuation, and more importantly, the associated sensitivities, provide the means by which the trader can make appropriate risk management decisions in order to maintain the value of a book of derivative transactions exposed to market volatility. The trader is charged with risk management to fulfil a duty to shareholders and other stakeholders. There is no requirement for objectivity in valuation as the risk factors can be a function of the institution itself.
Regulatory valuations
Regulatory valuations are those used by the regulator to define capital requirements. Regulatory valuations are increasingly becoming distinct from accounting valuations. For example, the regulator has disallowed DVA as a contributor to capital (BCBS, 2011a) and while this does not directly impact the valuation of individual trades it has affected the effective book valuation. The forthcoming Prudent Valuation regime (EBA, 2012; EBA, 2013a; EBA, 2014c) will require banks to calculate Additional Valuation Adjustments (AVA) to adjust the value of a trade down to that based on a the 90 % confidence level, given market price uncertainty. The adjusted value will be that used for regulatory capital purposes.
1.4.3 Summary: The Valuation Paradigm Shift
Different agents have different perspectives and drivers and the valuations they use will reflect this. Derivative pricing reflects manufacturing costs and these costs include CVA, FVA, MVA, KVA and TVA. Representatives of companies, including banks, are required to operate on a going concern basis and to factor in the management of all visible risk factors into valuations. Realism is an important element of trading valuations that have to reflect the actual cost of manufacturing derivatives. Derivative valuation theory is not invalid but has been shown to be out of date and hence needs to be updated to reflect market reality. This book aims to provide the required update.
1.5 Reading this Book
This book can be read in two ways. Firstly it can be read as a manifesto for the change in derivative valuation and the move away from the pure Black-Scholes-Merton framework. This is a controversial topic and will no doubt remain so for some time. The book can also be read as a practical guide to the calculation of valuation adjustments and it is therefore up to the reader what model elements are selected from those discussed.
The book is organised into five main parts. Part I discusses models for counterparty credit risk and CVA, while Part II discusses FVA models as an extension to CVA model. The regulatory capital framework and KVA model are introduced in Part III. The implementation of XVA models is discussed in part IV and this section of the book is aimed to be a practical guide for those who are building bespoke internal models as well as those who may be buying third-party systems. Finally Part V discusses the management of XVA principally through active hedging programmes.
PART One
CVA and DVA: Counterparty Credit Risk and Credit Valuation Adjustment
CHAPTER 2
Introducing Counterparty Risk
Take calculated risks. That is quite different from being rash.
2.1 Defining Counterparty Risk
Counterparty credit risk, sometimes known simply as credit risk or default risk, can be defined as the risk that a counterparty will fail to make payments that are due to another party. Consider a simple fixed rate loan in which the borrower makes annual fixed payments to the lender for five years before repaying the loan principal. The borrower defaults if they fail to pay any of the interest payments or the loan principal. The same is true for bonds and other securities, except the default will occur on payment to the securities holder. Derivatives also expose counterparties to credit risk. Some derivatives such as interest rate swaps involve bidirectional payments throughout their life which implies that both counterparties have default risk to each other, and that the direction of the risk changes during the life of the transaction.
Counterparty credit risk is only present when one counterparty has an exposure to the other. The exposure at default (EAD)11 is the total amount owed by the defaulting party to the non-defaulting party,
where V is the total value. There is no exposure if the non-defaulting party owes the defaulting party money and this gives the max function in equation (2.1). If the exposure is positive and the defaulting party owes the non-defaulting party money, this value will form the basis of the claim the creditor will make against the defaulter through bankruptcy proceedings. The expected positive exposure12 (EPE) is the expected exposure of party A to their counterparty B at some future date with the expectation or average taken over all possible future outcomes on the date of interest as defined in equation (2.2).13
The expected exposure profile is simply the expected exposure as a function of time. These exposure measures play a crucial role in the calculation of CVA. The expected negative exposure is the expected exposure that party B has to party A as seen from the perspective of A:
(2.3)
The
The
