How Interpolation Choices Shape Bootstrapped Yield Curves
Summary
Bootstrapping a yield curve from market instruments produces discount factors or zero rates at the instruments’ maturities. These observed maturities are curve nodes; they do not by themselves specify values at every date. An interpolation method fills in the points between nodes, creating the continuous term structure used for valuation and other calculations.
The document’s central lesson is that piecewise yield-curve types differ in what quantity they interpolate and how they interpolate it. The question names log-linear and cubic discount methods, linear and cubic zero-rate methods, and linear-forward and spline-cubic discount methods, but the answer does not explain their formulas or compare their behavior. It directs readers to a yield-curve construction reference for a fuller treatment. Thus, it clarifies the role of interpolation but does not provide enough detail to choose among methods or assess their effects on pricing.
Key ideas
- Bootstrapping gives market-implied curve values at the maturities of the input instruments.
- Those values are nodes rather than a complete curve over all dates.
- Interpolation determines the values between the bootstrapped nodes.
- Different piecewise methods interpolate different curve representations and can produce different intermediate values.
- The discussion points to a reference for further detail but does not give method formulas.
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# Explanation for Different Piecewise Yield Term Structures from QuantLib Python # Explanation for Different Piecewise Yield Term Structures from QuantLib Python I am new to QuantLib on Python, but as far as I understand, there are different types of piecewise yield term structures which exist on QuantLib which are bootstrapped on a number of interest rate instruments to create the zero curve. I refer to the following link: https://quantlib-python-docs.readthedocs.io/en/latest/termstructures.html#piecewise However, there does not seem to be a formula or a clear documentation for me to understand what exactly is the difference between the different piecewise yield term structures. The different piecewise yield term structures (interpolation methods) are as follows: - `ql.PiecewiseLogLinearDiscount` - `ql.PiecewiseLogCubicDiscount` - `ql.PiecewiseLinearZero` - `ql.PiecewiseCubicZero` - `ql.PiecewiseLinearForward` - `ql.PiecewiseSplineCubicDiscount` Can someone please provide me with an explanation and/or formula attached to numbers 1, 5, and 6 please? I did check the QuantLib Python Cookbook by Goutham Balaraman and Luigi Ballabio, and saw an explanation only for numbers 2, 3, and 4. Any help will be most welcomed, thanks. ## Answer by David Duarte (score 7, accepted) https://quant.stackexchange.com/a/66395 When you bootstrap a curve, you get discount factors/zero rates for the maturities of the instruments you supplied. So in practice, you get points, and not a "curve". After you have built your curve, which is made of nodes (dates and respective discount factors or zero rates), different interpolation methods will give you different results for dates that are NOT curve nodes. A good reference for different interpolation methods is Methods for Constructing a Yield Curve, by Hagan and West
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