**Abstract**

We consider the problem of finding the single-period fixed-income performance contributions of a generic security with a complex cash-flow structure. We extend the traditional fixed-income contribution model, based on the duration and the convexity, to include securities with generic floating-rate coupons and possibly with embedded call, put, or convertibility options. Using this method we can also compute the contributions of amortizing bonds and mortgage-backed securities and, as a special case, we also handle interest-rate only derivatives such as interest-rate futures. In this formulation we compute carry contributions exactly, i.e. without resorting to the traditional approach that the carry is proportional to the yield to maturity. Also in order to properly deal with the effect of the curve slope we define, for each security, a correction to the interest rate that summarizes the non-flatness effects. Finally and most importantly, we show how to compute the contributions of market-traded bonds with respect to their quoted price improving on the traditional approximation that is simply based on the model price.

**Keywords**: performance contribution, fixed-income attribution, bond pricing, interest-rate derivatives,

fixed-income securities, pricing functions, interest-rate contribution, credit contribution, cash-flow discounting, spread/rate contribution, carry contribution, convergence contribution, coupon contribution

**Pdf file**: fixed-income-contributions.pdf

## Marco Marchioro says:

Updated the paper to version 3.1