Credit Pricing and CVA
Overview
The price of a loan with credit risk, (that is a loan that could default), is less than the price of an
identical loan with no credit risk. The difference is termed the CVA, or credit value adjustment.
{% RiskyValue = RiskFreeValue - CVA %}
Measurement and Modeling
Define the loss on a loan due to default as {% L %}.
{% Loss = L %}
{% L %} can be decomposed into a set of factors. (see
pd, lgd, ead
or
td, lgd, ead)
The natural question to ask is what the relationship of {% CVA %} is to the statistics of {% L %}.
{% CVA = \mathbb{E}(L) ? %}
Assuing that losses are uncorrelated, one could argue using logic from the
Capital Asset Pricing Model,
that a large bank could diversify all the variability of its loan portfolio due to default, and hence the
{% CVA %} should equal {% \mathbb{E}(L) %}.
However, loan defaults are generally correlated to some degree. That is to say, there are market factors that cannot
be diverisified away that command a price. (see
credit portfolios)
