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• The Kalman filter is employed to separate these components historically as well as to identify the model’s optimal parameters. When applied retrospectively, the filter is able to estimate today’s value for (i.e. “initialize”) the diffusion term.
• AD&Co simulator preserves correct scales and orthogonality (mutual and serial independence) of random shocks that disturb the interest rates, the HPI diffusion, and the HPI jumps.
Modeling sub-prime deals backed by geographically dispersed collateral may require constructing geographical HPI models for states and even MSAs. We have reviewed several practical methods of achieving this goal. One of them, the “Alpha-Beta” approach, views the relationship between states and the US in a way resembling stock-to-an-index. It captures well the regional exposure to the US home prices, but leaves the question of modeling states having large idiosyncratic volatility open.
The other method, Principal Component Analysis (PCA), traces geographical home prices to 1-2 additional random variables that can be extracted mathematically. Our analysis has shown, after the US HPI index is accounted for, the second component can be interpreted as “economic swing”, the difference between dense economic centers and areas with available land.
Valuation methods
Regardless of the HPI generation process, the LDM model has two additional state variables: the delinquent and severely delinquent populations of borrowers (or, for a single loan, their probabilities). Therefore, we will be dealing with a large number of random variables thereby reducing the valuation choice to the Monte-Carlo method, even if the instrument in question is an unstructured loan or a pool of loans. Although Monte-Carlo is a relatively slow option, its convergence is not strongly affected by the number of variables. We expect to face several challenges when running Monte-Carlo for the credit OAS application:
• Credit models work better on loan-level data. When it’s available, a large number of loans in a pool can make computations slow.
