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The yield-price relationship is inverse, and we would like to have a measure of how sensitive the bond price is to yield changes.
A good approximation for bond price changes due to yield is the duration, a measure for interest rate risk.
For large yield changes convexity can be added to improve the performance of the duration.
A more important use of convexity is that it measures the sensitivity of duration to yield changes.
Similar risk measures used in the options markets are the delta and gamma.

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