Convexity
(1) In a fixed-income instrument, convexity is a measure of the way duration and price change when interest rates change. A bond or note is said to have positive convexity if the instrument's value increases at least as much as duration predicts when rates drop and decreases less than duration predicts when rates rise. Positive convexity is desirable to an investor because it makes a position more valuable after a price change than its duration value suggests. See Convex Payoff Function. (2) In an option position, convexity is a measure of the way the value of the position changes in response to a change in the volatility or price of the underlying instrument. A position with positive convexity (gamma) maintains or increases its value better than delta predicts when volatility increases or when prices change by a large percentage in either direction. An option position with negative convexity loses value relative to delta's prediction when prices change in either direction. Also called Curvature. The opposite of Concave Payoff Function. Convex Payoff Function. See also Gamma (1).
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