Inputs: Underlying: $18.00 Strike: $20.00 DTE: 8 Vol: 75% Delta: 0.1863 Gamma: 0.1341 Theta: -0.0336 Vega: 0.0071 Rho: 0.0007 Current Price: $0.20 How do I calculate the probability of this call option touching $0.50 prior to expiration?
Given the underlying's volatility, calculating the probability of it touching a price is straightforward. Calculating the probability of the option's price touching is much more difficult. You'd have to predict what the IV will be between now and expiry for one thing. The option price is determined by both the underlying's price and also the IV. In fact I'm assuming you're looking at a call so if underlying goes up, IV will probably go down, plus every day that passes you lose money due to theta.
If you want to do a simple approximation, calculate the price of the underlying at which the option will be valued at $0.50, assuming all else being equal. Once you have that, calculate the probability of the underlying reaching that price. All these things are likely to produce somewhat inaccurate numbers, at best, but at least it's smth. As the other poster said, there are lots of things that have an impact on the pricing of options.
Ok, so using the CBOE option pricing tool, I calculated this option would be worth $0.50 (today) if the underlying is >= $19.13 So how do I figure the probability of the stock touching $19.13 in the next 8 days? Mind two of those days are not trading.
I don't know how to calculate the probability of the option trading at $0.50. In general, the delta can be used as an estimate of the probability of the stock being over the strike at expiration. For your example, that would be 18.63%.
I have a reliable system that affects the price of options.. If I buy an option the price soon drops...but that's okay, because if I go short the price quickly rises! Well, at least it seems like that's the way it works.
You need to price an option on an option with a strike at 0.50. Then probability of touch is approximately 2*N(d2). Geske formula is often used for this. I can't find a free online calculator for this but Invest Excel has a spreadsheet that would work (comound options sheet), or I can post C code if you can use it. Martinghoul's suggestion is probably good enough as a rough approximaion, I would add that you should price it at a date about 2/3rds the way to expiry to balance rate decay and optionality decay.
Kevin, in real world you can't price a one-touch this way, you need to take into account the skew and term structure. There is a good BS-based approximation that you could use but that's beyond this thread
Uhm, it's not that easy because you will lose value through time... If IV stays at 75, than 5 days from now... only 3 dte... that call will have to be the ATM to have 50 cents value. So spot needs to be about 20 by then. If only 1 day left.. the IV needs to be >120 to get to 50 cents for ATM...
You're right. But its worse than that! My original intuition, essentially that you can price a one touch on an option the same way you price a one touch on a non-option underlying, is completely wrong. Thinking on it, I don't see any obvious closed-form model for it. A quick google search doesn't turn up anything either. It could be done with a simulation or tree -- incorporate skew, smile as in Haug, ignore vol term structure on near term option.