Read the expected move off a straddle price

Question

A stock trades at 100 with earnings tonight. The at-the-money straddle expiring this week costs \5. What is the market-implied expected move, and why does the straddle price measure it? Derive the approximation.

Accepted Answer

The ATM straddle pays ST - 100. Its price is therefore the risk-neutral expectation of the absolute move: 	ext{Straddle} = E\left[\,ST - K\,ight] = E[\,	ext{move}\,]. So a \5 straddle means the market prices an average absolute move of about \5, i.e. ±5%. The market thinks a close of 105 or 95 is a "typical" outcome; the straddle buyer wins if the stock moves more than 5, the seller if less. Where the common approximations come from. If the move is roughly normal with standard deviation \sigma{move}, then E[X] = \sigma{move}\sqrt{2/\pi} \approx 0.8\,\sigma{move}. Consistently, the Black-S…

Read the expected move off a straddle price

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