# Calculating the probability of a price change using an options pricing formula

I don't know if I'm doing this right and I'd greatly appreciate help. I'm trying to use an option pricing formula to backout the likelihood of the Euro dropping below $1.27, even for a minute, at any time by April 10. My calculations are in an excel worksheet labeled "Current" here: https://www.dropbox.com/s/sggti4iji5tjfne/binary-american-option.xlsx The formula is from here: http://www.matthiasthul.com/joomla/attachments/article/70/American%20Digital.pdf  3/25/2013 Today's Date 4/10/2013 End Date B= 1.27 strike price S0= 1.28652 spot price T= 0.043835616 time to strike date (years) sigma= 0.0896 volatility of underlying, measured in std dev of annual % change r= -0.001 risk free interest rate below this line calculated automatically alpha= -0.00501408 beta= 0.00301408 ratio= 0.987159158 logratio= -0.012923998 zscore1= -0.695973397 zscore2= -0.681887312 cumnormal1 0.243222745 cumnormal2 0.247655105 factor1 1.003224855 factor2 1.013007874 term1 0.244007103 term2 0.250876571 price 0.494883674  • So why do you think you aren't doing it correctly? Values aren't lining up with expectation? Syntax error? Also, no one wants to download a spreadsheet off the Internet like this; you'll be better served to paste your formula here on Stack Exchange. – chrisaycock Mar 26 '13 at 2:36 • Thanks Chris, post updated... I'm a novice so I'm wondering if anyone will point out mistakes or assumptions I didn't understand. – Michael Bishop Mar 26 '13 at 4:15 ## 1 Answer I you want to look at an option-pricing method, you would have to look at a down-and-in barrier option: Down-and-in: spot price starts above the barrier level and has to move down for the option to become activated. But the thing is, you do not have to look at an option pricing formula, you just need a model and a handle on probability theory. So, if you assume the classic Geometric Brownian Motion, then you will be able to find a close form solution in this article. • Note that this probabilty is under the risk free measure. – Bob Jansen Mar 26 '13 at 13:12 • @BobJansen not necessarily no.... You would use$\mathbb{Q}\$ only if you were willing to price an option. Using the GBM model is enough for him. – SRKX Mar 26 '13 at 17:39
• +1 but applying it isn't super-obvious to me so i'll wait to see if someone for whom its obvious is willing to walk me through it before i give out the check mark. thanks for getting me started :) – Michael Bishop Mar 26 '13 at 18:26
• @SRKX you're right, I'm assuming too much. Still a warning: do not mix measures! – Bob Jansen Mar 28 '13 at 19:40