### Wrong-Way Risk

In this chapter, the associated implications on exposure estimation and CVA determination by wrong-way risk (WWR) will be discussed and its causes identified. The quantitative approaches used will then be outlined. Moreover, we will analyze how collateral affects WWR and discuss the implications of central clearing.

When unfavorable dependence between counterparty credit quality and unfavorable exposure needs to be indicated, the phrase wrong-way risk (WWR) is generally used. In case the possibility of counterparty default is high, then exposure will be equally high, and the reverse is also true.

The manifestation of WWR can be potentially dramatic despite there being a reasonable assumption to ignore it. On the other hand, if the dependence between credit quality and exposure is favorable, then right-way risk exists. Counterparty risk and CVA will be reduced by a right-way risk situation.

# Overview of Wrong-Way Risk

## Simple Example

To get CVA, credit spread can be multiplied by exposure, while relying on the assumption that the different quantities are independent. Otherwise, the integration of credit risk quantification and market risk must be figured out. WWR has been significantly underestimated in the derivatives market, but as illustrated by 2007 market events, WWR can be extremely serious.

## Classic Example and Empirical Evidence

In economic regression, mortgage providers will face both falling prices of property and skyrocketing rates of default by homeowners. There are trades containing WWR across different asset classes in derivatives, namely:

1. Put option: A common WWR case is a put option purchased on a stock where fortunes, possessed by the underlying in question, are highly correlated to those of the counterparty.
2. FX forward or cross-currency products: Simultaneous deterioration of counterparty’s credit quality and a currency’s weakening should be the considerations of any FX contract.
3. Interest rate products: The link between the counterparty’s credit spread and the relevant interest rates are crucial considerations.
4. Commodity swaps: Price fluctuations exposed to the producer of a commodity may be hedged with derivatives.
5. Credit default swaps: The widening of credit spread of the reference entity may lead to an exposure when protection in a CDS contract is purchased.

A recession leading to an environment with both low-interest rates and high rate of default is described as a clustering of corporate defaults when interest rates fall.

## WWR Challenges

The link between collateral, credit, funding, and exposure is modeled through the quantification of WWR. This arrangement leads to the rise of the following challenges:

1. Uninformative historical data: Empirical data may fail to reveal WWR which may be subtle.
2. Misspecification of a relationship: Inappropriate specification of dependency.
3. Direction: The direction of WWR may not be specified.

# Quantification of Wrong-Way Risk

## Wrong-Way Risk and CVA

In the event of default by a counterparty, by representing the exposure conditional we can obviously achieve incorporation of WWR in the CVA formula.

Consider the following expression with $$E\left( { t }_{ i }|{ t }_{ i }={ \tau }_{ C } \right)$$ representing the expected exposure at time $${ t }_{ i }$$ conditional on this being the default time of the counterparty($${ \tau }_{ C }$$ ):

$$CVA=LGD\sum _{ i=1 }^{ m }{ EE } \left( { t }_{ i }|{ t }_{ i }={ \tau }_{ C } \right) \times PD\left( { t }_{ i-1 },{ t }_{ i } \right)$$

The heuristic approach of WWR quantification is supported by this equation when the probable increase in the conditional EE is assessed qualitatively compared to the unconditional one.

## Simple Example

A simple correlation parameter can be applied when expressing the link between exposure and counterparty default.

The conditional expected exposure, which is WWR, is increased by a positive correlation between the likelihood of default and exposure. On the other hand, right-way risk is due to a negative correlation.

## Wrong-Way Collateral

A high-quality government bond collateralizes a payer interest rate swap hence representing a general WWR situation as the increase in the value of the swap will be due to increasing interest rate and falling of collateral value.

On the other hand, beneficial right-way collateral is a reversal of the above position, experienced by a receiver interest rate swap. A more specific relationship between the credit quality of counterparty and the value of the collateral is due to cases of wrong-way collateral.

# Wrong-Way Risk Modeling Approaches

## Hazard Rate Approaches

A stochastic process for the credit spread can be introduced and correlated with other underlying processes necessary for exposure modeling, which is a procedure for modeling WWR.

The process of credit spread will lead to the generation of default and the computation of the consequent conditional EE will be in the usual way solely for default paths. Through credit spreads’ historical time series, and other market variables that are relevant, the observation of the necessary correlation parameters is possible.

## Structural Approaches

There is a separate mapping of exposure and default distributions into a bivariate distribution by using structural approaches. Just like the case with WWR, an early default time being coupled with a lower exposure is due to negative dependency, and the reverse is also true.

In this method, the merit is that the used exposure distributions are pre-calculated and WWR is essentially added on top of the existing methodology. However, the correlation parameter is opaque and hence difficult to calibrate which poses a drawback.

## Parametric Approach

Hull and White’s suggestion is that either an intuitive calibration should be used based on a what-if scenario, or the relationship calibrated through historical data by computing portfolio value for past dates. The link between this and the credit spread of the counterparty should then be examined.

The relationship is driven by the single parameter, with similar effects to the structural model’s correlation. The current counterparties’ trades’ portfolio should be naturally similar to the one applied in the historical calibration.

## Jump Approaches

With respect to historical default events, Levy and Levin were able to create an empirical approximation of the magnitude of the jump through the residual value of sovereign defaults currency.

Observations in the CDS market support the devaluation approach. Even though other currencies witness simultaneous quotes, the quoting of most CDSs is usually in U.S. dollars.

## Credit Derivatives

A simple model is applicable in the description of counterparty risk. It may be difficult to assess the effect of collateral as CDS risks are highly contagious and systemic, naturally. The fair price of purchasing or selling CDS protection is computed as a correlation function between the counterparty and the reference entity.

The reference entity CDS spread is taken as 250 bps and 500 bps for the counterparty CDS spread. Both LGDs are taken as 60%. The implication is a very strong correlation impact as a person buying protection, at 60% correlation, will be ready to pay around 200 bps contrary to the 250 bps paid with a risk-free counterparty.

## Wrong-Way Risk and Collateral

Due to the fact that an increase in exposure may result from WWR, it is very crucial to take into consideration collateral effects on WWR. But since it is timing-dependent, characterization is quite difficult.

Whereas a jump in exposure renders collateral to be of no use, a gradual rise in exposure before a default implies that there will be receipt of collateral. For a two-way collateral agreement, a curve of CVA drawn against the collateral rises with a positive gradient, when CVA is recomputed under the zero-threshold assumption. The reason the curve slope is quite shallow implies more collateral being generally taken.

As a result of the need to post collateral, when there is an extreme right-way risk, a negative impact exists in the relative benefits of collateral, and the benefits become greatest with the most WWR.

## Central Clearing and Wrong Way Risk

Central counterparties (CCPs) mainly aim to contain losses, from a clearing member’s default, within the clearing member’s committed-resources. They also have a tendency of disassociating exposure and credit quality.

In the definition of initial margin and default funds, quantification of the WWR component is challenging for significant WWR transactions.

The behavior of a central counterparty waterfall may be rather like a collateralized debt obligation (CDO), with the CDO’s first loss being covered by the defaulter initial margin and default funds, plus CCP equity.

A second loss position on the hypothetical CDO is possessed via the default fund contributions of clearing members and other loss allocation exposures. A CCP member is exposed to this loss position, and it is rather senior in terms of CDO. Based on their systemic risk exposures, these senior tranches are famous to be heavily concentrated.

Accepting a wide range of eligible security is the probable pressure CCPs are subjected to for the purposes of initial margin.

# Practice Questions

1) Which of the following statements is correct regarding general wrong-way risks (WWR)?

1. GeneralWWR are based on structural relationships that are not often captured via the real world
2. General WWR are difficult to model and risky to use given the naïve correlation assumptions
3. General WWR are based on macroeconomic behaviors
4. All of the above

Option $$C$$ is correct because general WWR are based on macroeconomic behaviors.
Option $$A$$ is incorrect. Specific WWR are based on structural relationships that are not often captured via the real world. Option $$B$$ is incorrect. Specific WWR are difficult to model and are risky to use given the naïve correlation assumptions.