### CDO Pricing: Binomial Expansion Technique

BET is a relatively simple technique used by Moody's to price and rate CDOs.

- First, the collateral pool is mapped to a hypothetical portfolio of N uncorrelated assets (
*the diversity score*). - The default probability of assets in the hypothetical portfolio is then calculated with WARF (
*Weighted Average Rating Factor*) .
- Since the default event of each asset is uncorrelated, the probability of
*J*defaults in the portfolio simply follows binomial distribution: (*DS*: diversity score.*PD*: probability of default for each asset) - With this distribution, the expected loss (EL) for each CDO tranche can now be calculated:
(
*L*: loss for a given tranche with_{j}*J*defaults) - The expected loss can now be used to price or rate the CDO tranche by referencing comparable securities (i.e. with similar default probability).

The BET methodology gives a sneak preview of what's deep down in the CDO pricing rabbit hole without getting into the rocket sciences (Monte Carlo, Copula, etc). Here is a good paper that compares the BET with Monte Carlo simulations.