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.

  • $\begingroup$ simulate interest rates, then build a model that links simulated interest rates to refinancing which is called S curve. $\endgroup$
    – adam
    Oct 26, 2016 at 13:07
  • $\begingroup$ Do you know what type of stochastic process people are using for the mortgage interest rate simulations? Some short-rate model or something? $\endgroup$ Oct 26, 2016 at 19:05
  • $\begingroup$ You don't model mortgage rate stochastically, you model interest rates. Mortgage rates are directly linked to interest rates. Anyways this is the industry standard for pricing $\endgroup$
    – adam
    Oct 27, 2016 at 15:27

1 Answer 1


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.

  • $\begingroup$ Thanks for the in-depth reply. That is precisely the sort of summary of the topic I was looking for. If I wanted to do Monte-Carlo simulations, should I be simulating the central-banking interest rates and then relating those interest rates to the mortgage rate with some sort of model / formula? Or is it just as valid to directly simulate the mortgage rate itself and not bother trying to model the central banking interest rates? $\endgroup$ Oct 27, 2016 at 16:12
  • $\begingroup$ That's a big "it depends" depending on what you are after. For the US look at simulating both UST and LIBOR (look at common ARMs to figure out which ones). I would use a fixed spread with a mortgage floor (ie, even if base + spread < floor use the floor). $\endgroup$
    – HerbN
    Oct 27, 2016 at 16:36

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