Price-Yield Curvature

Price-Yield Curvature, commonly known as convexity in fixed income and derivatives, measures the non-linear relationship between the price of an asset and changes in its yield or interest rate. Unlike a straight line, the price-yield relationship for most bonds and derivatives is curved, meaning the price changes at an accelerating rate as yields move.

In options trading, this is analogous to Gamma, representing how the sensitivity of the price to underlying movements changes as the market shifts. Understanding this curvature is essential for managing interest rate risk and portfolio hedging, as it quantifies the benefit or detriment of the non-linear price response.

When yields fall, the price increases at an increasing rate, and when yields rise, the price decreases at a decreasing rate. This convexity provides a cushion against adverse yield movements for long positions.

Traders use this metric to adjust their hedges dynamically to maintain delta neutrality. It is a fundamental concept in bond portfolio management and derivatives pricing models.

Without accounting for curvature, simple duration-based risk estimates would significantly underestimate price volatility. Effectively, it captures the second-order sensitivity of an asset price to yield fluctuations.