Outline the methods for modelling wrong-way risk: hazard rate, structural, parametric and jump approaches.
The idea
There are four ways to model wrong-way risk. In the hazard rate approach, the counterparty's hazard rate (credit spread) is stochastic and correlated with the market variables that drive exposure, so default is more likely in high-exposure states. In the structural approach, default occurs when firm value falls below a barrier, and the firm value is correlated with the exposure driver. The parametric approach imposes the dependence directly, for example by applying a multiplier to exposure or to CVA. The jump approach adds a discrete move in exposure at default, such as a currency devaluation when a sovereign defaults. Choose by the problem. Smooth correlation suits the hazard rate or structural models, while a gap on default needs the jump approach. The result is exposure conditional on default.
Formulas
CVA with a parametric wrong-way multiplier
CVA(WWR) = α × CVA(ind)
- α
- the multiplier for wrong-way risk, above one
- CVA(ind)
- the CVA computed assuming exposure and default are independent
Multiply, do not divide or add the multiplier. Simple, but it imposes the dependence rather than modelling its mechanism.
A practice question
In the hazard rate approach to modelling wrong-way risk, the dependence between exposure and default is introduced by:
- adding a fixed jump to the exposure at the moment of default, taken from a scenario.Why not: Describes the jump approach.
- making the hazard rate stochastic and correlated with the exposure's market variables. - correct
- multiplying the independent CVA by a constant factor chosen by the regulator.Why not: Describes the parametric multiplier approach.
- assuming that the default occurs when the firm value falls below a barrier correlated with exposure.Why not: Describes the structural approach.
The hazard rate approach keeps default as an intensity-based event but lets the intensity be a function of, or correlated with, the exposure's market drivers.
A harder one
A bank applies a parametric approach in which wrong-way risk is captured by multiplying the independence-based CVA by a factor of 1.25. The CVA computed assuming independence is USD 210,000. The adjusted CVA is:
- USD 168,000Why not: Divides by the multiplier instead of multiplying.
- USD 210,001Why not: Adds the multiplier as an amount instead of scaling the CVA.
- USD 52,500Why not: Applies only the uplift (alpha - 1) and drops the base CVA.
- USD 262,500 - correct
A parametric multiplier scales exposure or CVA: 210,000 x 1.25 = USD 262,500. It is simple but does not model the dependence itself.
The hardest tier
In a one-period hazard rate model there are two equally likely states of the market variable. In the low state the counterparty's default probability is 2% and the exposure is USD 2 million; in the high state the default probability is 6% and the exposure is USD 8 million. Loss given default is 60%. The CVA with the dependence modelled, compared with the CVA computed from the average exposure and the average default probability, is:
- higher, USD 156,000 against USD 120,000. - correct
- lower, USD 84,000 against USD 120,000.Why not: Reverses the dependence by pairing the low default probability with the high exposure, which is right-way risk.
- higher, USD 288,000 against USD 120,000.Why not: Applies the high-state default probability and exposure to the whole distribution, ignoring that the high state has probability one half.
- equal, at USD 120,000, since both approaches use the same average inputs.Why not: Averages the inputs before multiplying, which discards the dependence.
Dependent: 0.6 x (0.5 x 0.02 x 2 + 0.5 x 0.06 x 8) = USD 156,000. Independent: 0.6 x 5 x 0.04 = USD 120,000. The uplift of 30% arises from exposure and default probability being high together.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in CVA
- Account for why pricing counterparty risk is wanted and what makes it hard.
- Explain the concept of CVA, the adjustment made to a derivative's value for credit risk.
- Work out CVA, plus its expression as a spread, in the simple setting where wrong-way risk, netting and collateralization are all absent.
- Judge how shifts in credit spread and recovery rate assumptions affect CVA.
- Describe bilateral CVA (BCVA) together with debt value adjustment (DVA).
- Account for how unilateral CVA (UCVA) differs from BCVA, and how unilateral DVA (UDVA) differs from BCVA.
- Work out the DVA and the BCVA, then restate BCVA as a spread.
- Explain the way netting enters the computation of CVA.
- State what incremental CVA and marginal CVA are, compute them and show how CVA is turned into a running spread.
- Show how the CVA figure changes once collateralization is built in, paying attention to initial margins, thresholds and the margin period of risk.
- Spell out wrong-way risk and set right-way risk against it.
- Identify illustrations of right-way risk as well as wrong-way risk.
- Review how collateral bears on wrong-way risk.
- Identify cases that illustrate collateral exposed to wrong-way risk.
- Weigh up how wrong-way risk bears on CCPs (central counterparties).
- Account for what central clearing means for wrong-way risk.