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The first terms are duration and convexity, but are there common names for the terms beyond this?

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    $\begingroup$ I am not aware of specific 'jargon' for higher order derivatives in the bond pricing world. $\endgroup$ Commented Dec 5, 2022 at 7:58

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I don't like duration.

If the interest rates delta is the first derivative of the bond price with respect to the interest rates, probably by tenor bucket, and gamma is the second derivative of the bond price with respect to the interest rates, probably not a matrix but a risk-weighted sum as one number, then the interest rates speed would be the third derivative of the bond price with respect to the interest rates, or equivalently the rate of change in the interest rates gamma with respect to the interest rates.

Source: Espen Gaardner Haug. The Complete Guide to Option Pricing Formulas, 2E, pp. 47ff, in turn citing Mark B. Garman "Charm School," Risk Magazine, 5(7), pp. 53-56 (1992).

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There is no Mathematical jargon for such terms. However in particular applications a good understanding of what those terms do may warrant applications specific names such as the one mentioned by the previous poster in bond market. First order = linear approximation of whatever function or price you have. The rate of change being the Constant coefficient

Second order term = quadratic correction. Constant coefficient being the rate of change of the previous Constant coefficient

10 th order term = 10th order polynomial approximation. Constant coefficient being the rate of change of the previous (9th order) coefficient

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