Hi

@Arka Bose Good to hear from you! Right, the

*second statement is vexing*, to me also, I can't tell you that I yet have a full intuitive grasp of it. The first statement is the easy one: wrong-way risk is a positive (negative) correlation between exposure and default probability (credit quality). In this way, wrong-way (or right-way) risk is some dependence between exposure/EAD and PD. We normally write EL% = PD*EAD but that assumes independence between PD and EAD, so a way to think about WWR is simply when EL > PD*EAD, because EL <> PD*EAD is also a condition for non-independence. Okay, that the obviously true and easier statement.

Hi second statement he illustrates with this XLS

https://www.dropbox.com/s/qawyxfx0e8gb1z9/gregory-Chapter15.xlsm?dl=0 where I just added a page and snapshot below. Both have the same assumptions about a forward contract so the blue line is the "normal EE" for the forward contract. On the left is hazard rate (aka, instantaneous conditional PD) = 5% and on the right is hazard rate = 1%; i.e., the graph on the right reflects an

**increase in credit quality (from PD = 5% to PD =1%)**. Both graphs assume correlation, ρ(exposure, PD) = 50%. First, neither correlation nor hazard rate has any impact on "normal EE." They impact "wrong-way EE" which is the "conditional EE" being higher than the EE. Both of these panels are consistent with the first, easier statement: WWR is +50% correlation between exposure and PD. But we are now drilling into the first approach that

*could be used *to model the WWR. And this approach to quantifying WWR replaces the unconditional EE (ie, "normal EE" blue line) with a conditional EE ("wrong-way EE", red lines). So we are always here in a situation where WWR is represented by the positive correlation (eg, 50%) but he is is now referring to the quantification of WWR under the approach where a conditional exposure (EE) is calculated to quantify the WWR in the CVA model, and and under his model, the lower PD (1%) implies a higher WW EE line, which is indeed counterintuitive to me. And he explains thusly (emphasis and note mine):

"Let us look into this simple model in a bit more detail. Consider the impact of the counterparty default probability on the EE with WWR. Figure 17.2 shows the EE for differing counterparty credit quality, showing that the exposure increases as the credit quality of the counterparty also increases. **This result might seem counterintuitive at first, but it makes sense when one considers that for a better credit quality counterparty, default is a less probable event and therefore represents a bigger surprise when it comes.** [david: hmmm ... i see the math, but am not grokking the intuition still!] We note an important general conclusion, which is that WWR therefore increases as the credit quality of the counterparty improves." -- Gregory, Jon. The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital (The Wiley Finance Series) (p. 381). Wiley. Kindle Edition.

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