MODERN QUANTITATIVE FINANCE
Understanding XVAs
Seven members of the XVA family
X-Value Adjustment (XVA or xVA) is an umbrella term referring to a number of different valuation adjustments that financial institutions must make when assessing the value of derivative contracts that they have entered into. The ultimate aim is to adjust the risk-neutral derivatives valuation to account for real-world issues. Thus, XVAs are added onto base valuation models (like the Black-Scholes valuation model) because they are adjustments meant to account for real-world factors that traditional models ignore.
(i) CVA (Credit Valuation Adjustment) is an adjustment to the valuation of a derivative transaction which is made to account for the counterparty credit risk of contracting parties. CVA is calculated as the difference between the value of a portfolio which we assume is risk-free, and the same portfolio accounted for default risk. As such, CVA can be thought of as the market value of the counterparty credit risk for that portfolio. The higher your exposure to the credit risk, the higher your CVA, since you stand to lose more.
- A trading desk is a separately managed business line within a bank that follows defined trading strategies with certain instruments, aiming to generate revenues or maintaining market presence while managing risk. A change in CVA hits the trading desk’s P&L directly since CVA actually depends on a number of market-driven quantities. Now, because CVA is a P&L component, CVA desks are trading desks in many financial institutions.
- A CVA trading desk in a financial institution provides the internal service of quantifying the counterparty credit risk and using CVA to actively manage this risk.
- A credit risk model is used to get the CVA.
- The value of a purchased option contract is the value assuming no default (VND) less the CVA.
(ii) DVA (Debt or Debit Valuation Adjustment) is another counterparty risk metric, as it’s just the flip side of CVA. But, in the perspective of the option buyer, DVA is a metric reflecting the ‘risk of own default’ while CVA is a metric reflecting ‘counterparty credit risk’.
- The value of the option (as the liability to the option writer) is DVA less VND. In principle, CVA = DVA for a derivative that has unilateral credit risk such as an option contract. The difference is only in perspective — CVA is the credit risk facing the option holder whereas DVA reflects the credit risk of the entity that writes the contract.
(iii) KVA (Capital Valuation Adjustment) is a valuation adjustment that accounts for the cost of capital that a bank is required to hold to cover the risks of a derivative portfolio — particularly under regulatory capital requirements.
- So, capital requirements are priced into derivative trades via KVA.
(iv) FVA (Funding Valuation Adjustment) is a valuation adjustment to account for the [benefit] or [cost of funding a collateralized hedge] for a derivative desk in a derivative position. A net funding cost (FVA > 0) or benefit (FVA < 0) arises when uncollateralized over-the-counter (OTC) derivatives are hedged with centrally cleared contracts that require cash collateral. It is a cost when the bank posts collateral and a benefit when it receives the cash collateral.
- Physics-educated quant Dr. Christoph Burgard and Dr. Mats Kjaer shared the 2014 risk magazine’s quant of year award for publishing a paper which laid a sound theoretical framework to such a challenging concept.
(v) MVA (Margin Valuation Adjustment) reflects the cost of posting Initial Margin (IM) over the lifetime of a derivatives trade. Regulations require counterparties to post IM to mitigate default risk — since IM ensures enough excess cash is available at troubled times.
- But it was noted that even though regulations require counterparties to post mandatory IM to mitigate counterparty risk from bilateral trading, a trio of quants (Leif B. Andersen — Phd in Finance, Michael Pykhtin — PhD in Physics, and Alexander Sokol — Phd in Theoretical Physics) found that this doesn’t always effectively eliminate the counterparty risk. The trio shared the 2017 risk magazine’s quant of the year award for revealing hidden settlement risks and presenting solutions.
(vi) COLVA or ColVA (Collateral Valuation Adjustment) reflects the cost (or benefit) of posting Variation Margin (VM) or other forms of collateral during the life of a trade. This is because, in collateralized OTC derivative contracts, parties agree to post or receive collateral as market values change.
- While COLVA is crucial in the context of derivative trades due to the prevalence of collateral agreements, it can also be relevant in other scenarios where collateral is used.
- We note that COLVA can overlap with MVA.
(vii) LVA (Liquidity Valuation Adjustment) reflects the cost of liquidity risk associated with derivative positions — especially those positions which are harder to exit because there may not be enough buyers or sellers.
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Sources:
Understanding CVA, DVA, and FVA: Examples of Interest Rate Swap Valuation
