Interest Rate Sensitivity of Callable Bonds and Higher-Order Approximations

Certain fixed-income securities, such as callable bonds and mortgage-backed securities subject to prepayment, typically exhibit negative convexity at low yields and cannot be adequately immunized through duration and convexity-matching alone. To address this residual risk, we examine the concepts of bond tilt and bond agility. We provide explicit calculations and derive several approximation formulas that incorporate higher-order terms. With the help of these methods, we are able to track the price-yield dynamics of callable bonds remarkably well, achieving mean absolute errors below 2.5% across a wide variety of callable bonds for parallel yield shifts of up to ±200 basis points.