1
$\begingroup$

I'm relatively new to working with interest rate models and I am having some conceptual difficultly considering how a short-rate model can be utilized when calculating OAS of a mortgage-based bond, whose prepayment behavior will be based on longer term rates in any given month ($t$). For example, as a simple model assumption, a mortgage borrower might elect to prepay when 10 yr rates are 100 bps lower than their current coupon rate on the loan. A prepayment penalty calculation within the prepay model might also be based on current long term rates (such as the US10yr or US7yr).

In the context of a short-rate model this is my question specifically: if I calibrate a short-rate tree (such as BDT or Ho-Lee) then generate sample paths from this tree, can I infer a term structure of interest rates given a short-rate $r$ in a month $t$ at any point in the model/simulation?

$\endgroup$
1
  • 1
    $\begingroup$ Yes, a risk neutral short rate process defines all Bond prices along the modelled curve, be they short term or long term. See the remark and formula in wikipedia $\endgroup$
    – g g
    Jan 22, 2022 at 10:24

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.