First Duration, Then Convexity, Then What? Tilt?

20 Pages Posted: 6 Nov 2020

See all articles by James Angel

James Angel

Georgetown University - Department of Finance

Jiadi Chen

Georgetown University - Department of Economics, Students

Nikkie Pacheco

Georgetown University

Date Written: September 22, 2020

Abstract

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

Angel, James J. and Chen, Jiadi and Pacheco, Nikkie, First Duration, Then Convexity, Then What? Tilt? (September 22, 2020). Available at SSRN: https://ssrn.com/abstract=3697547 or http://dx.doi.org/10.2139/ssrn.3697547

James J. Angel (Contact Author)

Georgetown University - Department of Finance ( email )

McDonough School of Business
Washington, DC 20057
United States
202-687-3765 (Phone)
202-687-4031 (Fax)

Jiadi Chen

Georgetown University - Department of Economics, Students ( email )

Washington, DC
United States

Nikkie Pacheco

Georgetown University ( email )

Washington, DC 20057
United States

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