The Variance Risk Premium (VRP) is defined as:
$$VRP(t,t+\Delta t) \equiv RV(t,t+\Delta t)^2 - IV_t(t,t+\Delta t)^2$$
where $RV^2$ is the realized variance between $t$ and $t + \Delta t$ and $IV_t^2$ is the implied variance for the same period, implied as of $t$ (i.e. at the beginning of that period). We also lag RV back to line up with what was being implied.
I am unsure if I am getting the correct output. Below is the data, transformations and graph. Could someone confirm i am getting the desired output.
Secondly, if I would like to get the volatility risk premium, what is the conversion i would need to do?
Thank you in advance.
#The Data below is in volatility
tail(df) IV RVt_1 VRP 2021-06-28 0.1576 0.1197841 -0.010489536 2021-06-29 0.1602 0.1202760 -0.011197727 2021-06-30 0.1583 0.1225323 -0.010044727 2021-07-01 0.1548 0.1243042 -0.008511502 2021-07-02 0.1507 0.1257307 -0.006902284 2021-07-06 0.1644 0.1242254 -0.011595423
Where VRP = RVt_1^2 - IV^2. RV and IV in the database are in vols - Realized vols and implied vols
Lastly here are some of the stats.
mean(df$VRP) -0.005147035 median(df$VRP)-0.01194805
If I wanted to convert these to vols, can i take the absolute value before taking the square root?