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CONVEXITY Definition & Legal Meaning

Definition & Citations:

A mathematical measure that quantifies the sensitivity of an ASSET to large changes in price or YIELD. In OPTION contracts convexity (commonly termed GAMMA) measures the change in DELTA for a change in the price of the UNDERLYING; in FIXED INCOME products it measures the change in DURATION for a change in YIELD or INTEREST RATES. Mathematically convexity is the first derivative of a change in value with respect to duration/delta, or the second derivative of a change in value with respect to yield/underlying. Standard convexity calculations for a fixed income security with semiannual coupons are given by: where C is COUPON, t is the time to maturity, y is the semiannual yield, n is the number of semiannual periods, and M is the redemption value of the bond (generally PAR VALUE). Also known as OPTIONALITY. See also NEGATIVE CONVEXITY, NONLINEAR INSTRUMENT, POSITIVE CONVEXITY.

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