Bond Rate Sensitivities: Duration, Key Rates, and Rho
Summary
The document explains why bond sensitivities are commonly described with fixed-income measures such as duration rather than relying only on option-style Greeks. A bond’s value depends on a yield curve containing rates at multiple maturities, so its exposure is distributed across curve tenors. Key rate duration measures sensitivity to changes at selected points on that curve and differs from a single scalar sensitivity such as an option’s rho.
The described approach is to shift one yield-curve node, rebuild or interpolate the curve as needed, and reprice the bond to measure the effect. The impact of a node depends on cash-flow timing and the curve construction method; for example, a maturity between standard curve tenors can be affected by interpolation. The answer notes that convertibility, inflation linkage, and other features can add sensitivities beyond interest rates. It gives a conceptual overview, not formulas or a detailed treatment of curve risk aggregation.
Key ideas
- Bond interest-rate risk is commonly summarized with duration measures.
- Key rate durations describe exposure to changes at specific yield-curve tenors.
- A key rate sensitivity can be estimated by shifting one curve node and repricing the bond.
- Curve interpolation affects how a node change influences discount rates at other maturities.
- Convertible and inflation-linked bonds may have additional market sensitivities.
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# The most common Greeks for a Bonds and how do they work? # The most common Greeks for a Bonds and how do they work? I'm currently working on sensi (Greeks) for Bonds. I'm trying to understand how the Greeks are working for Bonds because the parameter used is the interest rate. I have learned that the Delta IR is a vector and it implies yield curve to compute it. Here the Delta IR is different from Rho (I don't understand why) But could someone give me some details please on it ? Thank you very much ## Answer by D Stanley (score 2) https://quant.stackexchange.com/a/82407 Bond analytics do not use the same "greeks" that other instruments like options do. The main "sensitivity" for fixed income securities is called duration, or sensitivity to underlying interest rate changes. As you have seen, though, bond analytics do not just use one "interest rate" in its valuation, but a time series of interest rates of various tenors (6M, 1Y, 2Y, etc.) called a "yield curve". Different bonds will have sensitivity to different rates along the curve. These are called "Key Rate" durations and are very important for bond analytics. How the price of a bond reacts to changes in these key rates will depend on how you model the price of the bond. They are typically measured analytically by changing the yield curve at one node and re-pricing the bond, taking into account any interpolation used to calculate the yields at non-key rate nodes. (e.g. if a bond matures in 1.5 years, how does changing the 1Y rate affect the yield curve used to discount cash flows?) Depending on the type of bond (convertible, inflation-indexed, etc) there may be sensitivities to other market data like stock prices and inflation expectations, but the primary sensitivity for bonds is interest rate sensitivity.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.