Hi Peggy,

Thanks for sharing that snippet, that's great. It is a subtle distinction: we can price the (present) value of an option with the riskless rate, and it will transfer to the risky world, but this is not true of N(d2) which is the PD. The PD [i.e., N(d2)], unlike option value, is not indifferent to the riskless state; it is lower in the risky world due to the expected return of the asset. I would still suggest that the step #2 above is not the option pricing model. Or let me put another way: it seems to me more intuitive that we use the expected return in estimating distance to default. Perhaps that is the "easier" part.

If you look at my practice question which applies the KMV (except for final step), it is pretty intuitively mechanical: grow the firm value, check distance to threshold in future, calculate probability. Does not require option pricing.

The harder part is: why is it that can we use the riskless rate when pricing the value of an option. This speaks to step #1; i.e., determining the value and volatility of the firm's assets. And I offer that we are using the riskless rate in only a very specific way: to compute the PV of the option, here being the equity of the firm.

1. I don't so much. FYI, it will not be tested. It is sort of a put option; i.e., if default, what is (debt) - (firm value), where this is LGD if firm value < debt. perhaps you can see the put in there? Then wraps the N() functions to probability adjust.

2. I attached PDF of a Basel reading that GARP dropped,

which I wish they had retained as give helpful perspective. Note they cite this correlation as an hot area for research (i.e., LDG & PD correlation; they like copulas for this).

The short answer is: no, Basel does not do this. They avoid it instead by making the formula conservative: (i) requiring the LGD be a "downturn LGD;" a lower-than-expected LGD for bad economic times and (ii) by rolling up all correlations into the single factor (ASRF). In short, the PD is "used" (abused, really) as it is translated from an expected loss PD into higher unexpected loss PD. If you think about the credit loss distribution, they "neglect" an LGD-PD correlation (which may reach heights of model arrogance/difficulty anyhow) in favor of pushing the UL out further to the right with downturn LGD and the single factor asset correlation which is given an almost comically large job.

Finally, you will note this is not Ong's UL. His UL is one standard deviation. As i mentioned in the newsletter:

* Ong UL = 1 s.d.

* Internal capital = UL at internal confidence

* Regulatory capital = UL per Basel IRB

And Ong has shown that correlation impacts UL but makes no difference to EL as it does not enter either individual EL ( = PD*AE*LGD) or portfolio EL (sum of component ELs). Thanks for diving deep on this, many of your insights will defintely show up in the cram session, you've noticed some cool connections!

David

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