I have a question on the estimation of earnings and ambient vol. Would appreciate if someone can clarify. For concreteness, consider MU, which has earnings on Sep 21. Looking through the option chain, we see that the aggregate IVs for the Sep 21, Sep 28, Oct 5, Oct 19, Nov 16 options are 0.56, 0.51, 0.48, 0.47 and 0.44, respectively. I want to use this data to compute the implied earnings and ambient vol. Since the earnings weight is always 1/DTE, we have the following equation to solve for the total IV given the ambient (AV) and earnings vol (EV):
IV^2 = 1/DTE * EV^2 + (1 - 1/DTE)*AV^2
Since we're given the IVs, we can solve for the EV and AV using a system of linear equations, one for each expiration (so I just used a generic solver). This gives me an ambient vol of around 0.39, and an earnings vol of around 1.88. Is this a valid approach?