An 8-trading-day option spans an earnings date and implies 65% volatility. The expiry that stops just before earnings implies 35% over its 7 trading days. Using 252 days a year, what one-day move does the market price for the earnings print?

An 8-trading-day option spans an earnings date and implies 65% volatility. The expiry that stops just before earnings implies 35% over its 7 trading days. Using 252 days a year, what one-day move does the market price for the earnings print?

Approach: Total variance adds across independent pieces. Strip out the diffusive variance of the ordinary days and attribute the remainder to the single event day.

10.0%. Total variance over the 8 days is 0.65^2*(8/252) = 0.013413, and the diffusive variance of the 7 ordinary days at 35% implied volatility is 0.35^2*(7/252) = 0.003403. Variance additivity leaves 0.013413 - 0.003403 = 0.010010 for the event, so the earnings move priced as one standard deviation is sqrt(0.010010) = 10.0%. The straddle itself pays the expected absolute move, which for a normal distribution is sqrt(2/pi)*10.0, or 8.0%, and that 8.0% is the number to compare against the stock's history of actual earnings reactions. Selling the event when the priced move sits well above the realised history is the classic trade, and it is short a large gap on the one day the distribution is not normal.

Follow-up: The stock has moved 4%, 5%, 12%, 3% and 14% on its last five prints. Do you sell the 8% and how do you hedge the tail?

Key concepts: variance additivity, event volatility, earnings move, implied volatility.