Mortgage Valuation: Modeling Prepayments and Interest-Rate Scenarios
Summary
The discussion outlines mortgage valuation as a problem of projecting cash flows under changing interest rates, borrower behavior, and discounting. A proposed simulation approach generates possible rate paths, calculates amortizing payments, and discounts the resulting cash flows. The response cautions against making refinancing automatic whenever rates cross a threshold: mortgages may remain outstanding despite favorable refinancing conditions, so refinancing should be modeled probabilistically.
The answer groups refinancing, home sales, and extra principal payments under prepayment, and identifies prepayment behavior as the main modeling challenge. It also notes that default is another relevant event omitted from the initial proposal. Rather than relying only on forecasts of future rates, the practitioner describes testing many possible rate movements to assess valuation across market scenarios. This is an introductory outline, not a complete model: it supplies no specific rate process, calibration method, borrower data, default model, or discounting framework.
Key ideas
- Mortgage valuation projects and discounts cash flows under multiple interest-rate scenarios.
- Refinancing should be modeled probabilistically rather than triggered with certainty by a rate threshold.
- Refinancing, home sales, and extra principal payments are all forms of prepayment.
- Prepayment behavior is a major modeling challenge, and default must also be considered.
- Scenario analysis across possible rate movements can support valuation without claiming to predict the next rate path.
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# General Framework For Valuing Mortgages # General Framework For Valuing Mortgages I am becoming more interested in mortgage valuation and would like some pointers on the basic valuation process for a mortgage. I understand there is likely an entire field of study devoted to valuing mortgages but I am looking to understand the basics. My thoughts so far: - Define starting mortgage financing rate, length of mortgage etc. - Monte-Carlo simulate mortgage rates (using which stochastic process?) - Within each simulated rate path, if the simulated rate drops to a new low by a certain threshold, assume a refinance at the new lower rate - Within each simulated rate path, calculate payments at each time step using Amortization equations and financed rate at that time step - Sum payments at each time step for each path, average across all simulated paths, discount to present Would something like this work? I guess it still doesn't account for default on the mortgage loan. Any pointers would be appreciated. ## Answer by HerbN (score 1, accepted) https://quant.stackexchange.com/a/30761 Some thoughts from someone whose group does mortgage servicing rights valuations: Even for a first pass your assumption regarding refinance is too deterministic. We have mortgages over a decade old that have never been refinanced. Without getting into a heavily data derived model you should at least give the refinance a probability instead of absolute occurrence. As you noted you didn't cover default but there is a third condition you didn't include which is payment of additional principle which can occur even with rates increasing. For that matter, refinance due to sale can occur with interest rates rising. Both of these plus the refinance option are all grouped together as prepayment. The figuring of the amortization schedule and discounting is straight forward. The big modeling is in the prepayment model. As for what people are using for the mortgage rate simulations I am used to do descriptive instead of predictive work. Instead of trying to guess future interest rates with do a few thousand different interest movements and price under each. This can be pretty computational intensive. What it does is allow those we support to have a good model of pretty much any real market moves the next day while they are making decisions. This Citibank presentation gives a pretty good overview and has a few references to get you started.
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