Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given historical implied volatility and all other know variables (stock price, option strike price, option expiration date, dividend rate, interest rate) what is the best way to calculate the probability of an option being in the money at expiration?

share|improve this question
You mean the delta? – chrisaycock Jan 27 '12 at 6:10
Why you need "historical implied volatility"? – Alexey Kalmykov Jan 28 '12 at 22:15

N(d2) is near to the probability the option will expire in the money; I have a video showing how d2 is similar to distance to default in the Merton here on youtube.

N(d1) is the delta.

The technical issue is that N(d2) is a risk-neutral probability; the input in d2 is the riskfree rate, although the theory is more involved.

But, if you replace the riskfree rate with a realistic drift (mu) you have a reasonable estimate, however N(d2) of course assumes normally distributed log returns. So, as with BSM, your answer here still makes the limiting assumptions, namely normal log returns and constant volatility. (I don't know what "historical implied volaility" is: the input is a current, instantaneous volatility estimate, it can be historical or implied)

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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