Let's assume that company XYZ reports earnings in a 0% interest rate environment and the option expires shortly after earnings. And there is a 50% chance the earnings are good (an upmove) and 50% bad (a down move)
historically, we see an average of a 2% move in the positive/negative after earnings with a SD of 4%
The expected value from 0 to infinity (good earnings)
Earnings with a bi-modal distribution
Can we re-price black sholes by multiplying the current price by (E) the expected earnings 'pop' percentage value, divide by 2 (50/50 chance of good or bad earnings), and discounting that from the strike?. So if E = .01 and the price is 400 and the strike is 420 our new strike is 418, hence the option is more expensive which confers with observations of options being more expensive before earnings?