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Mortgage Refinancing Decisions and the Value of the Prepayment Option

Article Quant Q&A · Author: Thomas Redding
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Summary

The document asks whether refinancing should be triggered by a simple comparison between lower interest payments and refinancing fees. It presents consumer heuristics for fixed-rate mortgages, including refinancing when market rates fall by a threshold or when expected payment savings recover the costs over the anticipated time in the home. Discounting and tax treatment can refine these calculations, but they still omit a key feature: the borrower’s prepayment option.

A more complete decision rule compares the present value of after-tax payment savings with refinancing costs plus the value lost by giving up the existing mortgage’s prepayment option. That option’s value depends importantly on the interest-rate term structure, so a lower current rate alone may not make immediate refinancing optimal. The document notes that ordinary heuristics do not capture this trade-off and that rigorous valuation may be beyond many consumers. It does not specify a stochastic rate model or provide a full quantitative procedure.

Key ideas

  • Simple refinancing heuristics compare rate reductions or payment savings against transaction costs.
  • Discounting and tax treatment can improve a basic cash-flow comparison.
  • A mortgage includes a prepayment option whose value affects the timing of refinancing.
  • The optimal decision compares after-tax savings with costs and the loss in option value.
  • The prepayment option depends on the term structure of interest rates.

Tags

Fixed incomeOptionsDerivatives pricingRisk management
Full text
# Is there a "standard" "textbook" model for making re-financing decisions?


# Is there a "standard" "textbook" model for making re-financing decisions?












You have a loan with an x% interest rate. Rates fall to y%. Should you pay a fee to refinance?

Presumably not if the NPV of the saved interest is less than the fee. However, if you always refinance whenever the NPV of saved interest is a mere 1¢ greater than the fee, interest rates could drop 10pp, and you'd end up making literal pennies, so a naive cost-benefit analysis is clearly useless.

So, as with the Black-Scholes model with options, and as with Markowitz/CAPM with stocks, is there a "standard" model for evaluating refinancing decisions? Maybe something like "assume mortgage rates follow a Brownian motion" model.

My Google-fu is epically failing me :(

## Answer by Sharad (score 3)

https://quant.stackexchange.com/a/78759

Assume that the loan in question is a fixed-rate mortgage. There are some standard heuristics recommended by consumer finance specialists which can be quite far from the "textbook" model (also known as optimal mortgage refinancing, as pointed out by nbbo2). These include refinancing when prevailing rates are at least 0.50% (50bps) lower than your current mortgage rate (earlier rules suggested a trigger of 2% but the costs associated with mortgage refinancing have generally trended lower over time) or a breakeven method which compares the cost of refinancing with the monthly payment savings realized over the expected tenure in the house.

Another layer of sophistication could be added to this analysis by discounting cash flows and by including tax considerations (specifically, the tax treatment of discount points and closing costs).

Still, neither of the above approaches consider the value of the prepayment option that the borrower receives when they hold a mortgage. In particularly, these approaches ignore the trade-off between paying an above-market rate right now and the "time value" of the prepayment option -- it may be better to refinance in the future as opposed to now. The optimal refinancing rule would say that one should refinance when:

PV(after-tax monthly savings) = Refinancing costs + Loss in option value

There is a loss in the value of the prepayment option we receive when we exchange the old mortgage for a new lower rate one because the old one is in-the-money whereas the new one is either at-the-money or out-of-the-money.

Of course, as nbbo2 also points out, the regular consumer does not typically have the sophistication/knowledge to value this prepayment option which depends crucially on the term structure of interest rates.

For a down-to-earth analysis of this issue, see Chapter 2 in A Financial Analysis of Consumer Mortgage Decisions.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.