Using Decimal Rates When Fitting Nelson–Siegel–Svensson Curves
Summary
The document explains the rate-unit convention for fitting Nelson–Siegel–Svensson curves to spot, forward, or discount rates. Its answer states that rates should be entered as decimals, such as 0.05 for a quoted five percent, rather than as whole percentage points. This convention supports consistent use of the model’s mathematical functions and calculations.
It also explains why a discount-factor expression divides the spot-rate output by 100: the rates in Svensson’s presentation are expressed in percentage units, so the division converts them to decimal units before applying the exponential calculation. The guidance addresses unit conversion rather than curve estimation choices. It does not discuss fitting algorithms, parameter constraints, compounding conventions, or how to handle datasets whose rates are already stored as decimals, so those details should be checked separately.
Key ideas
- Use decimal-form rates when fitting the NSS model.
- A quoted rate of five percent should be represented as 0.05 in decimal units.
- Dividing a percentage-form spot rate by 100 converts it before discount-factor calculation.
- The explanation concerns unit consistency and does not specify fitting or compounding choices.
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# Nelson-Siegel-Svensson: question regarding data format for fitting the model
# Nelson-Siegel-Svensson: question regarding data format for fitting the model
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.
## Answer by Sane (score 1)
https://quant.stackexchange.com/a/80202
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.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.