CVA basics

When the Basel Committee looked back at the 2007–09 crisis, it found that roughly two-thirds of the losses banks attributed to counterparty credit risk came from CVA, and only about one-third from counterparties actually defaulting. Banks lost money because their counterparties became more likely to default, and the market price of that risk rose. RiskAtoms Bank's two trades with Halvergate are worth nothing today on the trading desk's screens. Allowing for Halvergate's chance of default, they are worth £211k less.

The trading desk values a swap as if both sides will always pay: the risk-free valueThe value of a derivative as if neither side could default: what the book's pricing models give.. The counterparty might not. The credit valuation adjustmentCredit valuation adjustment: the risk-free value of a netting set minus its value allowing for the counterparty's possible default. The market price of counterparty risk. is the difference:

CVA is an expected loss, but a market one. It needs three things this module has already built. The expected exposure profile EE(t) from L3.4.02: Exposure measures: how much the bank expects to be owed at each future date. The chance that the counterparty defaults at each date, read from its credit spread with the hazard rates of L3.3.16: Market-implied default risk. And the share of the exposure lost, 1 − R. Multiply them date by date, discount, and add up.

Because CVA is part of a price, it uses risk-neutral default probabilities from CDS spreads, not the real-world PDs of internal ratings. Most counterparties have no traded CDS: a mid-sized manufacturer, a hedge fund or a pension scheme rarely does. Banks then assign a proxy spreadA spread used for a counterparty with no traded CDS, taken from liquid peers of similar rating, industry and region. from liquid peers with a similar rating, industry and region. The book's spreads for Halvergate, Saltney and Ebbsworth are best read as proxies of this kind.

The book's CVA

Three things stand out. Saltney has the largest CVA, £958k: a big exposure (the bought put is worth about £19m today) and the widest spread. Corriemoor, with a tighter spread than Halvergate, has a larger uncollateralised CVA (£384k) because its trades are much larger. And collateral changes everything: under the CSAs, Saltney's CVA falls to £35k and Corriemoor's to £53k. What is left is the margin period of risk from L3.4.06: The margin period of risk. Ebbsworth keeps more (£128k) because its CSA has a £10m threshold. Across the book, CVA is £1.83m with no collateral and £426k as the CSAs actually stand.

CVA is computed on the netting set, not trade by trade, since close-out netting (L3.4.04: Netting) means only the net amount is lost. IFRS 13 allows exactly this: a bank that manages its exposure to a counterparty on a net basis may measure the credit adjustment on the net position.

The other side: DVA

The bank can default too. DVADebit valuation adjustment: the mirror image of CVA, the value to the bank of its own possible default on what it owes the counterparty. is CVA seen from the counterparty's side: the same formula applied to the negative expected exposureNegative expected exposure: the average of max(−V, 0), what the counterparty expects to be owed by the bank., with the bank's own spread. Accounting fair value includes it (IFRS 13 counts the entity's own credit risk in the value of its liabilities), so a bank's profits rise when its own credit worsens. Regulators strip that gain out of capital, and the Basel CVA framework works with CVA alone. For Halvergate, with RiskAtoms Bank's own spread at an illustrative 80bp, DVA is £93k and the bilateral CVABilateral CVA: CVA minus DVA, the net adjustment when both sides' default is priced. is £118k.

Written out, with $\tau$ the counterparty's default time, $E(t) = \max(V(t), 0)$ the netting set's exposure (after collateral where there is a CSA) and a grid $0 = t_0 < t_1 < \dots < t_n = T$:

The survival curve $e^{-\lambda t}$ is continuous decay (M-A05: The number e and continuous growth). Its density is $f_\tau(t) = \lambda e^{-\lambda t}$, so the PD of each slice is the fall in survival across it. The third line assumes that the exposure on the day of default is no different, on average, from any other day. When that fails, it is wrong-way risk (L3.4.11: Wrong-way risk).

Two approximations. With one point per year at mid-year, $\text{CVA} \approx (1-R)\sum_{y} \text{EE}(y - \tfrac12)\,\text{DF}(y-\tfrac12)\,\text{PD}(y-1, y)$: for Halvergate this gives £214.4k against £210.7k on the half-month grid. And because $(1-R)\lambda = s$, for small $\lambda t$:

The spread approximation is 9% high because it ignores that Halvergate may already have defaulted before the later dates. It explains why CVA is close to linear in the spread and nearly blind to the recovery assumption.

Pick a netting set, move its spread and recovery, and switch its CSA on and off. The EE profiles are the book's full 2,000-path simulation, computed once on the server; only the CVA sum runs as you move the sliders.

Accounting. IFRS 13 defines fair value as an exit priceFair value under IFRS 13: the price that would be received to sell an asset, or paid to transfer a liability, between market participants at the measurement date. between market participants, so derivative values must reflect the counterparty's credit risk (CVA) and, for liabilities, the entity's own non-performance risk (DVA). Its portfolio exception (paragraphs 48 and 56) lets a bank measure the adjustment on the net exposure to a counterparty, taking account of netting agreements.

Capital. Basel III added a capital charge for CVA risk after the crisis losses in the hook. Today's framework (MAR50, in force from 1 January 2023) offers a basic approach, BA-CVA, in a reduced form with no hedges and a full form that recognises CDS hedges, and a standardised approach, SA-CVA, built on sensitivities like the ones in this lesson, which needs supervisory approval. Regulatory CVA excludes DVA. A bank with €100 billion or less of non-centrally cleared derivatives may simply set CVA capital equal to its counterparty credit risk capital. The detail is in M4.3: Market risk capital (FRTB) and CVA; DVA, funding and the other valuation adjustments (XVA), with full exposure simulation, are in M6.6: Counterparty risk and XVA.

• CVA is the risk-free value minus the risky value: the market price of the counterparty's possible default.
• CVA = (1 − R) Σ EE(t) × DF(t) × PD(t−1, t), with PDs from the CDS (or proxy) spread; Halvergate's is £211k.
• Collateral cuts CVA sharply: Saltney £958k to £35k, Corriemoor £384k to £53k.
• CVA ≈ spread × discounted exposure: nearly linear in the spread, nearly blind to the recovery assumption.
• CVA moves daily with spreads and exposures (CS01), so it is a market risk; DVA is its mirror image, excluded from capital.

CVA

Credit valuation adjustment: the risk-free value of a netting set minus its value allowing for the counterparty's possible default. The market price of counterparty risk.

Risk-free value

The value of a derivative as if neither side could default: what the book's pricing models give.

DVA

Debit valuation adjustment: the mirror image of CVA, the value to the bank of its own possible default on what it owes the counterparty.

Bilateral CVA

Bilateral CVA: CVA minus DVA, the net adjustment when both sides' default is priced.

Negative expected exposure

Negative expected exposure: the average of max(−V, 0), what the counterparty expects to be owed by the bank.

CS01

CS01: the change in CVA when the counterparty's credit spread rises by one basis point.

Proxy spread

A spread used for a counterparty with no traded CDS, taken from liquid peers of similar rating, industry and region.

Exit price

Fair value under IFRS 13: the price that would be received to sell an asset, or paid to transfer a liability, between market participants at the measurement date.