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Valuation Commentary - May '07
First steps in Credit OAS (part II)
by Alex Levin
Last month’s Valuation Commentary introduced the concept of valuation under concurrent prepayment and default modeling. The main idea is to use stochastic home price index as an additional modeling factor and pass it to the LoanDynamics™ Model (LDM). The LDM then responds by projecting CPR, CDR and losses, among many other outputs, for each market scenario.
This month’s article draws on these ideas and discusses valuation of sub-prime deals containing thousands of loans. We take a look at a Countrywide deal, CW0708, as a case study. This deal has 4,304 (1,756 fixed rates and 2,548 ARMs) sub-prime, first-lien, mostly new loans. We will focus on measuring “price of losses”, the expected present value of the lost cashflow stream. This value points to the expected provision for losses that a bank has to set aside.
Smart Monte-Carlo
With the required analytics in place, how would we process a large inventory? This issue is faced by anyone who would like to set-up Monte-Carlo runs for portfolios containing multiple positions, loans or securities. In order to make the right choice, we must ask ourselves: “Do we really need to assess the value of each position accurately, or are we more interested in an accurate summary?” In most practical cases, the answer will be the latter, rather than the former. Indeed, when accurate valuation results are required for trading purposes, focus is made on a few positions, the trade candidates and their hedges. Residential loans are almost never traded separately, so the focus of a portfolio run is likely to be the portfolio’s summary.
In this case there exists a simple and effective method: use a few Monte-Carlo paths per position and start each position’s run from random seed. It turns out that, from the portfolio’s standpoint, this approach is equivalent in accuracy to a lot of independent Monte-Carlo runs. The efficiency depends on the homogeneity of the loans. Imagine, for example, that collateral consists of 1,000 perfectly identical loans. Running 2 random paths per loan seeded randomly is equivalent to running 2,000 random paths, from the portfolio’s standpoint. In contrast, running 2 random, but the same, paths per loan, is no different than running only 2 paths for the portfolio.
