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Convexity

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Convexity
A Bond’s convexity is the amount that its price sensitivity differs from that implied by the Bond’s duration. Fixed-rate bonds and swaps have positive convexity: when rates rise the rate of change in their price is slower than suggested by their duration; when rates fall it is faster. Positive convexity is therefore a welcome attribute. The higher the Bond’s duration, the more its convexity. Bonds or swaps with call options or embedded call options, eg collateralised mortgage obligations, have negative convexity: when rates rise their price fall is faster relative to the Interest rate move. Convexity effectively describes the same attribute as Gamma.
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