For a stock trading at $27, $28 strike, 0% interest, 15% annual vol, and one day until expiration there is about a 1 in 17000 chance of it being exercised?

$d_2 = \frac{1}{.15\sqrt{1/252}}\left[\ln\left(\frac{27}{28}\right) + \left(0 - \frac{.15^2}{2}\right)(1/252)\right]$

$1/(0.5 (1 + Erf[(Log[27/28] - (1/252) (0.15^2/2))/(0.15 *2^{1/2} Sqrt[1/252])]))$

that seem way too small but it's the answer I got


With $15\%$ annual volatility we have $15\%/\sqrt{252}\approx0.94\%$ daily volatility. To go from $27$ to $28$ is a $1/27\approx 3.7\%$ move which is $3.7/0.94\approx 3.9$ standard deviations. For a normal distribution this is about $0.005\%$ probability which is in line with your result.

  • $\begingroup$ Nice answer, practical, concise and to the point. +1 for this!!! $\endgroup$
    – Matt
    Jul 15 '13 at 6:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.