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Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i.e. how the duration of a bond changes as the interest rate changes. [3] Specifically, one assumes that the interest rate is constant across the life of the bond and that changes in interest rates occur evenly.
Duration is a linear measure of how the price of a bond changes in response to interest rate changes. As interest rates change, the price does not change linearly, but rather is a convex function of interest rates. Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes.
Specifically, duration can be formulated as the first derivative of the price with respect to the interest rate, and convexity as the second derivative (see: Bond duration closed-form formula; Bond convexity closed-form formula; Taylor series). Continuing the above example, for a more accurate estimate of sensitivity, the convexity score would ...
Bond convexity is a measure of the sensitivity of the duration to changes in interest rates, the second derivative of the price of the bond with respect to interest rates (duration is the first derivative); it is then analogous to gamma. In general, the higher the convexity, the more sensitive the bond price is to the change in interest rates.
In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order terms ) of the modeling function.
The modified duration formula assumes a linear relationship between percent change in return and percent change in price; but because returns compound, it overestimates the actual change in price. This difference is called "convexity".
Bond convexity; Bond convexity closed-form formula; ... Bond duration closed-form formula; Bond equivalent yield; C. Clean price; Coupon (finance) Coupon rate; Coupon ...
Analyzing Duration, Convexity, DV01 and Key Rate Duration. At banks. The assessment of interest rate risk is a very large topic at banks, thrifts, saving and loans ...