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TL;DR

In fixed income, the second derivative of bond price with respect to yield: it measures how duration changes as rates change. More generally, convexity refers to the curvature of a payoff or price function.

By Valenke Exam Prep Team·Last updated 2026-06-03

Convexity

In fixed income, the second derivative of bond price with respect to yield: it measures how duration changes as rates change. More generally, convexity refers to the curvature of a payoff or price function.

Why it matters for interviews

Convexity determines whether a position benefits from large moves (positive convexity = long gamma) or suffers (negative convexity). Options have convex payoffs; understanding convexity is essential for both fixed income and derivatives.

Definition and Mathematical Foundation

In fixed income, the second derivative of bond price with respect to yield: it measures how duration changes as rates change. More generally, convexity refers to the curvature of a payoff or price function.

Application in Quantitative Finance

Convexity determines whether a position benefits from large moves (positive convexity = long gamma) or suffers (negative convexity). Options have convex payoffs; understanding convexity is essential for both fixed income and derivatives.

Related Terms

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Frequently Asked Questions

Why do long option positions have positive convexity?▼
The option payoff is a convex function of the underlying. By Jensen's inequality, \( E[f(X)] \geq f(E[X]) \) for convex f. This means volatility is beneficial -- the more the underlying moves, the more the option is worth.
What is negative convexity?▼
Mortgage-backed securities exhibit negative convexity: when rates fall, prepayments increase (limiting price appreciation); when rates rise, prepayments slow (amplifying price decline). The price-yield curve is concave.
How does convexity relate to gamma?▼
Bond convexity is the fixed income analog of gamma. Both measure curvature. Positive gamma/convexity means the position benefits from large moves in either direction.