# Volatility basics: what happens to implied volatility of stock in week of earnings and dividend payment?

Question: Imagine it is a Monday. Company A (stock you are following) has an upcoming dividend payment on Wednesday and an earnings announcement on Thursday. Company A stock is currently trading at \$10; dividend will be \$5. The implied volatility of the call option (strike = 10, expiration = Friday end of day) is 30 vols. These are American options.

(a) Qualitatively explain what might happen to the implied volatility in the above scenario. How might you go about thinking whether the volatility level is fair? (b) If a put option (strike = 10, same expiration at call) was offered in the market at the same vol reference of 30 vols, what would you do (if anything)? Why?

Attempt:

(a) My only experience with equity options volatility calculations is by doing simple 'weighted-average' calculations. That is, for our 5 days, I would think about doing something like: $$\sigma_{\text{implied}} ^2 = \frac{1}{5}\sigma_{\text{Monday}} ^2 + \frac{1}{5}\sigma_{\text{Tuesday}} ^2 + \frac{1}{5}\sigma_{\text{Wednesday}} ^2 + \frac{1}{5}\sigma_{\text{Thursday}} ^2 + \frac{1}{5}\sigma_{\text{Friday}} ^2$$

This was asked as a question to talk aloud through (so no access to calculators, computer, etc.) so then perhaps we make the assumption that the volatilities for Monday, Tuesday, and Friday are equal to some baseline daily volatility level $$\sigma_B ^2$$. Then we can make the assumption that the volatility on the day of earnings $$\sigma_E ^2$$ will be greater than the volatility on the day of the dividend payment $$\sigma_D ^2$$, so the equation becomes:

$$\sigma_{\text{implied}} ^2 = \frac{3}{5}\sigma_{B} ^2 + \frac{1}{5}\sigma_{D} ^2 + \frac{1}{5}\sigma_{E} ^2$$

Then, as we go throughout the week, there will be a greater weighting on the earnings day and the dividend payment day and thus the volatility will increase up until dividend payment, after which it will decrease for the Friday. For example, on Tuesday morning the above equation may look like:

$$\sigma_{\text{implied}} ^2 = \frac{2}{4}\sigma_{B} ^2 + \frac{1}{4}\sigma_{D} ^2 + \frac{1}{4}\sigma_{E} ^2$$

Then for part (b), I don't really know how to think about the question.