Note: please do note that I am a tech person with no economics background.

I've been studying short-rate models so much for interview purposes and finally took a step out of the weeds to think about what I'm doing. All these mathematical finance books talk about the short-rate as stochastic processes that take on values amongst the real numbers and whatnot, but how does the 'lumpy' effects of monetary policy come into play for these models, either theoretically or in the workplace?

Do models get recalibrated every time there's a Fed announcement? I am studying models that are too basic, and there actually are models that include some sort of probability of a rate raise/cut as input? I understand the short-rate is not actually the same as the Fed rate because the former is a hypothetical, super-super-super-short-maturity rate but surely the rate has an extremely high probability of taking on certain numbers based on possible decisions by a central bank?

  • $\begingroup$ What is your academic background? Are you acquainted with stochastic differential equations with jumps? $\endgroup$ Commented Oct 5, 2023 at 10:30
  • $\begingroup$ @RodrigodeAzevedo Aw man I missed the notification so I'm guessing you won't see this, but I have a regular finance degree so no, I'm not very good with SDEs (although I'm trying to self-study towards it) $\endgroup$
    – Five9
    Commented Oct 14, 2023 at 21:00

1 Answer 1


Essentially, yes. The interest rate that the central bank pays on reserves held with them is a policy variable. It is not dependent on bond markets or investor confidence.

The central bank, as it has done many times, adjusts their target interest rate as a policy tool. They believe it's best suited to ensure price stability. This policy decision impacts both short term and long term rates.

I would highly recommend diving into the New Economic Perspectives website. Starting here, with this blog series, you can see the below figure. It shows historic moving averages for 10-year and 3-month Treasury rates less GDP growth. The bars represent averages for these two series for three time periods.

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The conclusion here is that during the Fed's higher target rate period between about 1979 and 2000, these yields followed suit. They were dictated, not by market growth (GDP, etc), but by the policy decisions of the government and central bank.


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