This will be our defaults in this model.

And because the model is so simple,

transition probabilities in this model are simple to compute,

so the whole default thing should be easy, right?

And actually, it's not right at all.

Such events simply cannot happen in the GBM model,

because in this model, the zero level is inaccessible.

In other words, the GBM model is incompatible with default,

they cannot occur in this model.

And this practice, of course,

known to everyone who studied financial engineering, but

implications of this factor are rarely discussed, so let's talk a bit about it.

If defaults cannot occur with the GBM model,

we should say that the model is wrong in a worst case, or incomplete in a best case,

which would essentially be more or less the same but just differently phrased.

Corporate defaults are rare events with probabilities of the order of 1% or

so, but awareness of these events is very essential to the markets.

If these events are ignored by the markets,

then credit spreads will be equal zero, which is solely not the case.

So credit markets and their observable, such as press or credit default swaps,

or CDS, which we discussed earlier in this facilitation,

indicate that these events are taken into account by the market,