First Duration, Then Convexity, Then What? Tilt?
20 Pages Posted: 6 Nov 2020
Date Written: September 22, 2020
Standard treatments of the impact of interest rate changes on bond prices include duration and convexity. These concepts derive from the first and second derivatives of a Taylor series expansion of an option-free bond price as a function of interest rates. Does the third derivative matter? This paper derives the formula for the third derivative- based term, which we call tilt, and explores its properties. Tilt tells how quickly the convexity changes. Similar to the properties of duration, a higher yield reduces tilt, a longer maturity increases tilt, and a higher coupon reduces tilt, ceteris paribus. Tilt adds little to the accuracy of the impact of small interest rate changes for default-free option-free bonds. Tilt becomes interesting for bonds with embedded options such as callable bonds and mortgage-backed securities. Such bonds can experience rapidly changing convexity and price under certain interest rate regimes.
Keywords: Duration, Convexity, Tilt, Bond Prices, Embedded Options, Mortgage-Backed Securities
JEL Classification: G10
Suggested Citation: Suggested Citation