I am a beginner in financial risk management and recently I have been studying the plain vanilla interest rate swap.
I came across several articles talking about DV01 of interest rate swap as follow.
\begin{equation} DV01(t) = \frac{\partial V_{swap}(t)}{\partial R_{fix}} = \sum_{j=1}^N \alpha_j Z_t(t_j) \end{equation}
My question is: In the equation, $R_{fix}$ should be in decimals. Then for a 1 basis point (i.e. $1/10000$) change in $R_{fix}$, shouldn't it lead to a $(1/10000) \sum_{j=1}^N \alpha_j Z_t(t_j)$ change in the price of the interest rate swap?
Thank you.