 This approach is simple in principle but can lead to operational difficulties.It requires 

For these reasons, a pricing model-based approach to attribution may not be the right one where data sourcing or reconciliation is an issue.An alternative solution is to perform a Taylor expansion on the price of a security formula_1 and remove higher-order terms, which gives

formula_2

Writing the return of the security as

formula_3,

this leads to the perturbation equation

formula_4

where the last term denotes higher-order corrections that may be ignored, and

formula_5

formula_6

The terms formula_7 and formula_8 measure first- and second-order interest rate sensitivity.