Linker Duration
Yield duration in Chapter 6 is defined as the sensitivity of the fixed-income bond price to a change in the nominal yield to maturity. Inflation-indexed bonds require that we focus on why the nominal rate changes and distinguish between a change in the real rate and a change in the inflation rate. Let's start by formalizing the stylized linkers, keeping close to the notation of Chapter 3. Let the nominal rate be y, the real rate r, and the inflation rate i. Also, let the number of periods to maturity be N, the fixed coupon rate c, the par (or face) value of the linker FV, and the current price PV. For these stylized linkers, we are on a coupon payment date so there is no accrued interest to sully the equations.
P-Linker valuation ...
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