Thursday, October 25, 2007

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: (Lj: loss for a given tranche with 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.