XVA. Green Andrew

presence of holding costs the assumptions underlying the Modigliani-Miller theorem are violated. Regulatory costs, through capital requirements, act as holding costs leading to the direct consequence that Modigliani-Miller does not apply to derivatives and hence to FVA. Furthermore it is clear that there is no single risk-neutral measure that spans the market and that no two market participants will agree on price. Hull and White (2012b) maintain that FVA should not be charged; however, the market as a whole has reached the opposite conclusion with numerous banks taking reserves for FVA, including a headline-grabbing figure of $1.5bn by J.P. Morgan in January 2014 (Levine, 2014).

      1.4.2 Different Values for Different Purposes

      The so-called law of one price argues that the same asset must trade at the same price on all markets or there is an arbitrage opportunity. For example, if gold trades at $X on market A and at $Y on market B and X < Y, in the absence of transport and other cost differentials all trades will take place on market A. The question is whether or not this argument applies to OTC unsecured derivatives markets.

      Superficially it would appear that the law of one price should apply to unsecured derivatives if the term sheet for the transaction is the same across multiple banks. However, the terms under which those trades actually take place, that is the ISDA agreement, are frequently different so even in legal terms the trades are different. Add in the counterparty risk of dealing with the banks on an unsecured basis and it should be clear that each deal done with a different bank is different. If two banks offer the same derivative an arbitrager will find it very difficult to arbitrage them by taking opposite positions because of counterparty risk and capital considerations. Most unsecured derivatives are actually traded with corporate customers who use them to hedge balance sheet risks. Often the corporate will use hedge accounting rules and be focused on cash flows while the bank will use mark-to-market accounting. Many of these derivatives will be transacted one way round as corporates use the derivatives as a hedge on a natural risk. For example, many corporate fixed rate loans are structured as a floating rate loan with an interest rate swap in which the corporate receives the floating rate and pays the fixed rate. Derivatives transacted with corporates will also be frequently difficult to novate to a third party, particularly for trades with smaller corporates as they may have few banking relationships or indeed may have only one banking relationship. Other banks, particularly those from outside of the geographical region, may be reluctant to perform the credit analysis and know your client checks necessary to establish a relationship. The law of one price simply does not apply in such circumstances.

      A useful analogy to consider when thinking about derivatives is that of the manufacturing industry. Consider manufacturing cars; all cars are designed to carry passengers and luggage but we clearly do not expect them all to cost the same. Cars have different designs and features and these feed into the price. The value of the car will depreciate at different rates after the purchase. The cost of the car is driven by a wide variety of factors including the cost of components, labour costs, transport costs, etc. In general the price will be determined by

      Why should derivatives be any different?

      What is a Derivative Price?

The price of a derivative is just the price at which the transaction is dealt. For unsecured derivatives the price achieved is the end result of a negotiation process, which lies in sharp contrast to exchange traded derivatives where prices are determined by supply and demand in a very liquid market. As a negotiation both parties will try to reach an agreed price that satisfies the needs and expectations of both parties. Figure 1.2 illustrates the negotiation process.

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.

      It 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