# Statistical Inference of Variance Risk Premia

Good afternoon,

I am currently following Carr and Wu (2009) to compute variance risk premia from options written as (RV-EV)*100 for the payoff of a long var swap position. Now I want to see whether my computations are statistically significant by using the Python code:

reg = smf.ols('df ~ df',data=df).fit(cov_type='HAC',cov_kwds={'maxlags':22})
reg.summary()


with df being my timeseries of variance risk premia*100. The standard errors I receive are way too small (e^-16) so I assume my regression "model" is wrong. I also tried

reg = smf.ols('df ~ 1 + df',data=df).fit(cov_type='HAC',cov_kwds={'maxlags':22})
reg.summary()


But the SE is again way to small for my df.

I never worked with HAC stanard errors before and just recently found the code for it. I guess it is super trivial but does someone know how to compute the standard errors with a lag of 22-day length for the time series/VRPs?

• Your formula is odd. I think you should do something like ‚x~y‘, no? Mar 27 '21 at 18:00
• That is my problem. I dont know what to regress on, when I simply want to say that my variance risk premia are stat. significant/different from zero. Usually I'd compute my t-stat with '(\mu - 0) / \sigma' with sigma being my sample standard error. Since my SEs are autocorrelated I need to use the HAC method to compute robust SEs but this requires a regression and as I said I dont know how my model should look like to obtain legitimate SEs. Mar 27 '21 at 18:16
• Regress on a constant (i.e. [1 1 1 1 ...]) specifying the HAC option. Then the coefficient will be the mean and the SEE of the regression will be desired robust standard error. Mar 28 '21 at 0:56
• Thanks again. I resolved the issue. The question can be closed. Mar 28 '21 at 13:46
• Hi, maybe you can answer the question yourself for future reference? Mar 29 '21 at 11:28