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If I want to fit the Nelson-Siegel-Svensson (NSS) model to a set of spot, forward, or discount rates, my intuition says that the data should of course be in percentage form.

For example, I should use $r = 0.05$, instead of $r = 5$, as they are often quoted.

Is this correct?

Additionally, why does Svensson divide the spot rate by 100 when computing the discount factors, if the spot rate formula is already in percentage form ?

$$ d(m;b) = \exp\left( - \frac{i(m;b)}{100} m \right) $$

where:

  • $i(m;b)$ is the spot rate.
  • $m = T - t$ is the time to maturity.
  • $b = [\beta_0, ... , \beta_3, \tau_1, \tau_2]$ is the NSS parameter vector.
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When fitting the Nelson-Siegel-Svensson (NSS) model to spot, forward, or discount rates, it is important to use rates in decimal form rather than percentage form. This is due to the fact that the NSS model relies on exponential functions and other mathematical operations that require rates to be expressed as decimals.

In Svensson's paper, spot rates are divided by 100 because they are initially presented as percentages. This conversion is necessary because the model calculations and fitting processes require the rates to be in decimal format, even though they are often quoted as percentages in practical contexts.

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