Revised Fixed Rate Mortgage Prepayment Model.

Wesley Phoa, Ph.D.
President of Research

In redesigning the model, we took the opportunity to make both the modeling process and the prepayment assumptions as transparent as possible. Prepayment models available from brokers or software vendors are often black boxes; and relying on a black box for duration estimates and prepayment forecasts can be very dangerous when it stops working, as vividly demonstrated in 1998. Model risk cannot be eliminated; and it can only be mitigated by opening up the model and its assumptions.

Prepayment models are, by their nature, complex. The present article can only provide a very brief summary of how the new model works and the motivations behind its design. A fully detailed publication is in preparation and should be available by the time this article appears in print.

Prepayment modeling at Interactive Data Fixed Income Analytics
Research at Interactive Data Fixed Income Analytics is not an academic endeavor, but is tightly focused on the needs of our clients. In particular, the new prepayment model was designed with the following key objectives in mind:

• Accurate durations and cashflow forecasts
• Ability to create user customized models
• Ability to analyze model risk

It is worth saying a few words about each of these goals in turn. First, the question of accuracy is more subtle than it appears. The key point is that mortgage durations are accurate to the extent that they forecast price changes correctly. In other words, the correct reference point is the market itself, not forecasts generated by brokers or vendors (an obviously circular criterion). Provided Interactive Data Fixed Income Analytics durations continue to be consistent with observed empirical durations, clients can be confident that duration estimates and return simulations are meaningful and useful.

Second, user customization is essential. Any mortgage research group has limited resources relative to the size and heterogeneity of the US mortgage market. Interactive Data Fixed Income Analytics aims to provide reliable models for all major asset classes, but many investors will own specialized assets which we do not attempt to model. In the current version of BondEdge, various methods are provided for scaling the Interactive Data Fixed Income Analytics prepayment assumptions; the ability to tailor the model will be radically expanded in future releases.

Third, the ability to quantify model risk has become increasingly important. This analysis is not an abstract exercise in statistics, but must involve varying the model assumptions in a way that has a concrete meaning in the real world: for example, how are prepayments affected when refinancing costs drop, or when housing turnover rises? The model itself must be designed to make this kind of analysis possible.

Model structure and sample results
The new model is broadly similar in structure to the current model, but allows for much more intuitive and fine-grained control. The Interactive Data Fixed Income Analytics approach to prepayment model design has been described in numerous papers, and follows the normal market practice of estimating a non-interest rate sensitive component ("relocations") and an interest rate sensitive component ("refinancings") separately. The model-specific details, as laid out in Figure 1, allow for maximum flexibility in estimating each of these components.

Figure 1: Components of the new prepayment model

Non interest rate sensitive prepayments

• Relocations: smoothed PSA-like profile
• Defaults: smoothed SDA-like (Standard Default Assumption) profile
• Curtailments: constant CPR
• Adjustment for atypical points paid **

Interest rate sensitive prepayments

• Based on comparison with estimated mortgage rate
• Estimate uses current and long term mortgage spreads
• Comparison with estimated ARM rate-disincentive **
• Adjustment for prepayment penalty **
• Adjustment for atypical points paid **
• Refinancing threshold, or "elbow"
• Sharpness of response beyond threshold
• Absolute maximum level of refinancings
• Prepayments slow down when mortgage rates are very high

Burnout estimation

• Burnout based on refinancings experienced todate
• Maximum possible extent of burnout
• "Cure" based on weighted average time since refinancing *
• "Media effect" when mortgage rates reach historical lows *

Special adjustments to forecast speeds

• Short-term historical prepayment pattern *
• Seasonality adjustment to non interest rate sen- sitive prepayments
• Coupon/vintage specific effect *
• Pool specific effects *
• 
  

* Feature to be activated after initial 4.0g release
** Feature to be activated after initial 4.1g release

Parameter estimation is still in process, but testing has been carried out based on a translated version of the current prepayment model assumptions. Sample results are shown in Figure 2, and show rather clearly that the current assumptions have been broadly accurate over time, but that further tuning may be possible. The additional flexibility built into the model permits this.

Figure 2: Current model assumptions vs. history, 8% FNMA30

Figures 3 and 4 show two kinds of prepayment model risk analysis: historical and prospective. Figure 3 shows actual historical prepayments versus those which would have been generated by the model by varying a single parameter (refinancings triggered by availability of a 1% interest rate saving) while keeping the others fixed. This kind of analysis helps determine reasonable historically determined bounds of uncertainty for model parameters. Figure 4 shows prepayment vector forecasts generated using different assumptions about the long-term average spread between the 30-year mortgage rate and the 10-year Treasury yield; the current yield curve, and all other model parameters, are kept fixed. This kind of analysis helps measure the concrete impact of model risk on a security.

Figure 3: Model risk analysis interest rate responsiveness

Figure 4: Model risk analysis - long term mortgage spread forecast

Development cycle
The beta release of BondEdge 4.0 includes an implementation of the new model. However, to accommodate users who will be running versions 3.2g and 4.0b concurrently, the model assumptions have been tuned to resemble those currently used in BondEdge 3.2, corresponding to the parameters most recently revised in November 1998. However, there will be some shortening in estimated durations for high coupon mortgages.

More thoroughly revised model parameters will be released at the time of the general release of BondEdge 4.0, improving model durations for high coupon and highly seasoned mortgages. These are still a focus of current research, and feedback from clients is being actively solicited. Additional features will be progressively activated between the 4.0 and 4.1 releases, and after the 4.1 release, as indicated in Figure 2. As always, our desire to fine-tune the model is continually balanced against our desire to avoid disruption to our clients. Clients will be kept fully informed about any planned changes to model assumptions.