Modelling Prepayment

Liquidation prepayment happens because:

• Refinancing (lower mortgage interest rates).
• Loan is modified (adding principal balance).
• Property is sold.
• Borrower/homeowner defaults.
• More.

Prepayment (adversely) affects:

• Pricing of MBS pools.
• Replacement assets in CMB.
• Reinvestment risk if investor in NHA MBS.
• Administrative burden of reporting.
• Etc.

Products/Offerings contigent on predicing prepayment (accurately):

• Prepayment swap.
• Interest only (IO) strip.

The Linear Liquidation Model also known as the LLM

• The current industry benchmark.
• Adopted in November 2014.
• Replaced the Canadian Liquidation Vector aka CLV.
• Assumes that liquidation rate starts at 1% annualized and increases at a constant rate until it reaches 12% annualized at maturity for a typical 5-year fixed mortgage.

The LLM is a simple model - both a strength and a weakness.

Why not use the LLM?

RBC Capital Market (February 5, 2016) reports:

Liquidation speeds in recent years have exceeded prepayments estimated by linear liquidation model. […] The lender type (bank vs. nonbank lenders) also appears to be determinants of refinancing propensity. NHA MBS originated by bank lenders have been liquidating much faster than the ones originated by nonbank lenders.

In short, the LLM considerably underpredicts prepayment rates.

Stylized (empirical) fact: pool type matters.

Stylized (empirical) fact: Seasonality matters.

To be broadly consitent with the LLM, our prepayment model depends on the following factors:

• Seasonality (month of the year)
• Remaining term (months until maturity)
• Lender type (bank, credit union, aggregator, etc)
• Origination (the issuer)
• Pool type (975-pools vs 867-pools, etc)
  

The (academic) abstract might read something like this:

To forecast prepayment, we use a generalized additive model (GAM) with the Tweedie (compound Poisson-Gamma) distribution as the link function and splines on the covariates (month and remaining term).

Think of modelling prepayment as insurance or rainfall during the year.

The challenges:

• a substantial proportion of prepayment (claims/rainfall) at zero.
• a range of positive prepayment (claims/rainfal) for others.

The Tweedie used extensively in actuarial science to handle this type of zero-inflated distributions.

All models are wrong, but some are useful – George E. P. Box (Statistician).