What is the right way to express the change in interest rate time series, if this time series contains both positive and negative rates?

  • $\begingroup$ Current rate minus previous rate? $\endgroup$ – Chris Taylor Aug 9 '17 at 17:04
  • $\begingroup$ how about proportional change? i am trying to estimate tail risk and am hoping to generate time series that follows normal distribution $\endgroup$ – 291890964 Aug 9 '17 at 17:17
  • $\begingroup$ Proportional changes don't make sense if rates can be zero or negative. $\endgroup$ – Chris Taylor Aug 9 '17 at 18:06
  • $\begingroup$ Yes, sir. Hence my question. How do I deal with this? $\endgroup$ – 291890964 Aug 9 '17 at 18:16
  • $\begingroup$ Use current rate minus previous rate. $\endgroup$ – Chris Taylor Aug 9 '17 at 19:42

The usual approaches used to deal with negative interest rates are:

a) the normal (Bachelier) model or Brownian motion, where $dr_t = \sigma dW_t$; this makes changes independent from the level of the interest rate,

b) shifted lognormal (displaced diffusion) model, where, instead of the ordinary Geometric Brownian Motion $dr_t = r_t \sigma dW_t$, we have $dr_t = (r_t + h) \sigma dW_t$ with for example $h=2\%$ or any similar value accepted by convention or made to fit the data; this keeps changes somewhat proportional to the rate level, while allowing negative values up to $-h$.

You can also look at this question, which has useful references.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.