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Valuation Commentary - April '07
First steps in Credit OAS (part 1)
by Alex Levin and Will Searle
With the LoanDynamics™ Model (LDM) out the door (http://www.ad-co.com/credit_product_line/loan_dynamics_model.htm), AD&Co is at full steam working on its most needed application – incorporating LDM into our valuation/OAS system. “Credit OAS” is a natural jargon, perhaps very inaccurate, but serving its point: everyone understands what it means. We talk about an OAS model with a full generation of random loan losses and deals’ credit triggers. Capable of generating prepayments and defaults concurrently, coupled with our term structure models and home price index (HPI) model, the Credit OAS system should assess value and risk of sub-prime loans and structured deals in a fundamentally sound way. Our development ideas and first results are discussed in this article; read more on this topic in next month’s commentary.
Two-factor world, many states
Consideration of defaults and losses involves home prices (HP). Prepayment is a call option on a borrower’s loan. Default is a put option letting the borrower exchange his/her home for the outstanding loan balance. Both interest rates and home prices are factors in this decision. Technically, both prepayment and default are American-exercise options, but, respecting irrationality in individual decisions, we model them as a sequence of European payoffs.
Before we ask the LDM to forecast prepayments and defaults, we must tell it what will happen with interest rates and home prices. The interest rate dynamic is generated by AD&Co’s term structure library that is free of arbitrage and tied to swap rates and the swaption volatility matrix. The HPI dynamic was described in our April 2006 Pipeline article (http://www.ad-co.com/newsletter/Issues06/Apr06.htm), and presented in greater detail at the 2006 AD&Co conference (http://www.ad-co.com/secure/2006%20ADCO%20Presentations/HPI%20Model.pdf). Below is a summary:
• US HPI growth rate is generated by a dynamic stochastic model that includes 3 main components: the interest rate component pointing to the housing affordability, “diffusion” associated with other economic factors, and “jumps” in returns of the housing stock.
