in parallel, across all maturities twist measures the degree to which the curve has steepened or flattened. For instance, one might measure the steepness of the Australian yield curve as the difference between the 10-year bond future yield and the 3-year bond future yield. curvature (or butterfly, or curve reshaping) measures the degree to which the term structure has become more or less curved. For instance, a yield curve that can be fitted to a straight line exhibits no curvature at all. To describe these movements in numerical terms, typically requires fitting a model to the observed yield curve with a limited number of parameters. These parameters can then be translated into shift, twist, and butterfly movements – or whatever other interpretation the trader chooses to use. This model is often used for extrapolate CDS. Two of the most widely used models are polynomial functions and Nelson-Siegel functions (Nelson and Siegel (1987)). Here, polynomial functions are usually of the form where is maturity, are parameters to be fitted, and is the yield of the curve at maturity . Nelson-Siegel functions take the form where and are as above, and , , and , are parameters to be fitted via a least-squares or similar algorithm (see Diebold and Li [2006]; Bolder and Stréliski [1999]): is interpreted as the long run levels of interest rates (the loading is 1, it is a constant that does not decay); is the short-term component (it starts at 1, and decays monotonically and quickly to 0); is the medium-term component (it starts at 0, increases, then decays to zero); is the decay factor: small values produce slow decay and can better fit the curve at long maturities, while large values produce fast decay and can better fit the curve at short maturities; also governs where achieves its maximum. Svensson (1994) adds a "second hump" term; this is the Nelson–Siegel–Svensson (NSS) model. The additional term is: , and the interpretation is as for and above. Another generalizing of Nelson-Siegel is the family of Exponential Polynomial Model ("EPM(n)") where the number of linear coefficients is free. Once a curve has been fitted, the user can then define various measures of shift, twist and butterfly, and calculate their values from the calculated parameters. For instance, the amount of shift in a curve modeled by a polynomial function can be modeled as the difference between the polynomial parameters at successive