# LO 32.6: Calculate the stressed CVA and the stress loss on CVA.

LO 32.6: Calculate the stressed CVA and the stress loss on CVA.
Stress testing CCR for market risk events looks at the losses in market value of a counterparty exposure due to market risk events or credit spread changes. Financial institutions typically only consider the unilateral CVA for stress testing, which looks at a counterpartys default to the institution under various market events. However, financial institutions should also consider the possibility that they could default to their counterparties, and, as a result, should consider their bilateral CVA (BCVA), which is discussed in LO 32.7.
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2018 Kaplan, Inc.
Topic 32 Cross Reference to GARP Assigned Reading – Siddique and Hasan, Chapter 4
To calculate the stressed CVA and the stress loss, lets first look at the formula for calculating CVA. The following is a simplified formula for CVA that does not factor in wrong-way risk:
CVAn = LGD*n x EE* (tj) X p d ; (th , tj)
T
H
where:
LGDn = risk-neutral loss given default EE* (tj) = risk-neutral discounted expected exposure PDn(tj_l5tj) = risk-neutral marginal default probability
When aggregating across iV counterparties in a portfolio, the formula for CVA becomes:
N
T
CVA = ^ 2 LGD* x ^ EE* (tj) x PD* (tj_,, tj)
n=l
j=l
The components of this formula all depend on market variables, including credit spreads, market spreads, and derivatives values. Calculating a stressed CVA involves applying an instantaneous shock to these market variables, which could affect the discounted expected exposure or the risk-neutral marginal default probability. The stressed CVA can then be calculated as:
N
T
CVAS = J 2 LGD*n x y ; EEsn (t,) x PDsn (tH , t,)
11=1
j=l
The stress loss is simply the difference between CVAS and CVA.
Stress testing CCR in a credit-risk framework has similarities with stress testing in a market- risk framework. Both rely on EL as a function of LGD, exposure, and PD. Nevertheless, their values will differ depending on whether the view is from a market-risk or credit-risk perspective. The two primary differences include the use of risk-neutral values for CVA (versus physical values for ELs), and the use of ELs over the transactions life for CVA (versus a specific time horizon for ELs).
In addition, CVA uses a market-based model for calculating the PD. The market-based approach has the advantage of being able to incorporate a correlation between the exposure and the PD. This correlation can significantly influence the CVA. Because there is uncertainty regarding the correlation, financial institutions should run stress tests to determine the effects on profit and loss from incorrect correlation assumptions.
2018 Kaplan, Inc.
Page 247
Topic 32 Cross Reference to GARP Assigned Reading – Siddique and Hasan, Chapter 4
S t r e s s T e s t i n g D e b t V a jl u e A d j u s t m e n t