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Published: 25th March 2017 by William Webster

**Adjustments to value**

XVA refers to several different valuation adjustments that may be applied to derivatives. These adjustments have come about because the 2007/8 crisis caused us to question traditional models used to value trades. For example, the Libor based yield curve became significantly higher than a curve based on a “risk free” rate like the overnight index swap curve. The adjustments include:

**Credit Valuation Adjustment (CVA):** This adjusts value for the risk that the counterparty will default. A positive mark-to-market value on a derivative, if uncollateralised, gives you a credit exposure on your counterparty. That credit risk has a value associated with it. This depends on the deal net present value, default probability and loss given default of the counterparty. Risk modelling is difficult as it requires estimating the potential future value of the trade.

**Debit Value Adjustment (DVA): **This adjusts value for the risk that your bank will default. If you are incurring a loss on a derivative trade and you defaulted, then your counterparty may lose a proportion of their profit. Their loss depends on the deal net present value, your default probability and your loss given default. In theory, this is a credit to your bank’s other creditors.

**Funding Benefit Adjustment (FBA):** This adjusts value for the implied benefit of upfront payments on derivatives. When a bank receives an upfront payment, there is a benefit if the bank’s own cost of funding is higher than the rates used to calculate the upfront amount. (It is getting cheap funding).

**Funding Cost Adjustment (FCA):** This adjusts value for the implied cost of upfront payments on derivatives. Where a bank makes an upfront payment, there is a loss if the bank’s own cost of funding is higher than the rates used to calculate the upfront amount. (It needs to finance the payment with expensive borrowing).

**Collateral Valuation Adjustment (CoVA):** This adjusts for the cost/benefit of interest on cash collateral. In theory, collateralised trades don’t give you credit exposure. But cash paid as collateral receives the OIS rate. This may have a valuation benefit or cost depending on your cost of borrowing. Similarly, cash received may have a benefit or cost associated with it. This means that optimising collateral use (which may include other forms of asset) can have significant benefits to individual banks.

**Margin Value Adjustment (MVA):** This adjusts for the cost of providing initial margin. This is relevant to cleared trades where initial margin is continually required to support trades.

**Capital Value Adjustment (KVA): **This adjusts for the cost of regulatory capital required to support a trade. Even fully matched trading portfolios require capital (the capital requirements on equal and opposite trades with different counterparties do not net out). Subjectivity is inevitable - estimating future capital makes assumptions about the future course of regulation.

**Some Issues**

Some of these issues have been known about for over 25 years. For example, funding variation margin payments on futures can lead to a bias in pricing.

In theory valuation adjustments are sensible in that they allow you evaluate the price of risk.

However, there is an important issue around whether price and value are the same thing.

Price is what the market charges, value is what you think something is worth based on the risks it contains. The two things do not have to be identical. Differences may result from a host of reasons. For example, if your funding costs are high cash collateral paid will be expensive. This could make long dated derivatives potentially costly to you. Knowing about the size and nature of this is helpful to decision making. It also indicates why traders are making money. Is it because your bank is a relatively good credit risk?

The challenge today is to determine how much detail is relevant, how easy it is to get the data and then model what may happen.

**This is not unlike funds transfer pricing. Simple in theory but practicality difficult. All models will inevitably be approximations and should be used to discuss the nature of what you do but not act as the sole determinate of the way you do things.**

25th March 2017

Derivatives are traditionally valued by taking the expected future cash flows and then discounting them in accordance with interest rates to give today’s value (present value). Implicit is the assumption that the derivative contract will run to its contractual date and all the cash flows will be paid and received. However, in the real world this may not occur. The counterparty may default.

20th September 2009

When two parties agree to enter an interest rate swap (IRS) one party pays a fixed rate of interest and the other a variable rate. The variable rate is often referenced to Libor or Euribor. The interest payments are based on a notional amount, (with IRS no principal amount changes hands). In the market there are conventions for calculating the interest payments. For example USD IRS use an annual actual 360 interest rate calculation for the fixed payment and a quarterly or semi annual actual 360 calculation for the floating payment. Maturities are normally between 2 and 20 years but it is possible to trade swaps that have maturities exceeding 50 years. Customers using swaps to hedge can expect a dealer to quote a dealing spread. The dealer will want to receive a higher fixed rate than the one they pay. It's one way the dealer makes money from trading. Dealers will insist before trading that the appropriate documentation is signed. For swaps standard documentation is provided by the International Swaps and Derivatives Association (ISDA). This document is called a master agreement. It covers all swaps between the two parties. Individual transactions are then agreed by confirmation which refers to the master agreement.

25th March 2017

The valuation of assets and liabilities appears to be straightforward but isn’t. The problem centres on market liquidity and the information that is available. In actively traded markets, where there is proper depth, liquidity and transparency valuation using current market prices should prove robust.