Hi Say I purchase an OTM option today and forecast that the underlying will move X% within 7 days there must be a way to calculate what my return will be if the underlying makes its move in 1 day, 2 days 3 days etc by taking in to account how much the premium I paid has depreciated due to time. Is this essentially what the black-scholes model does? <b>Basically what I am asking is, how do you use Theta to forecast an options premium given a % change in the underlying.<b></b> Thanks, Ben
You do not use theta as such but yes, a model such as Black Scholes will forecast the price of an option of a given strike on a future date as a function of forecast price of the underlying and forecast implied volatility and days to expiration. You will need to estimate the implied volatility on the future date, as well as the price of the underlying, because obviously the price of the option will be higher if the underlying is swinging wildly at that time, independently of the price level the underlying is at. Theta is normally quoted as one-day time decay on a given day for an underlying unchanged price and as such, you cannot integrate it over a longer period. It is not a stable value and will be a different value completely on later days after the underlying moves. I suppose you could use it in a very rough way along with delta if the underlying has not moved much, but it is better to just recompute the value of the option from the model using your forecast of the underlying and implied volatility on the future date.
Using an options calculator is the easiest way to go about this. http://www.cboe.com/tradtool/IVolService7.aspx
I think the most important question here is by trading this option, what exactly are you trying to trade? Are you only concerned about being long delta? Are they any other risk factors you care about? Without that information, it's really tough to actually give you an answer.
Thanks for your help guys, very useful information. @slickpick Yes the goal is to take a long position selling the option back once the price has risen.
First off, you should have sold the opposing otm contract, instead of buying yours, jk. Yeah, just use any pricing model (BSM is fine) and input your parameters, with the days-to-expiration being the variable. I would start by using the prevailing vol as your input, then you can adjust it up/down to see price changes, just don't get cute and assume price and vol will move your way. From there, I would plot the option's premium given price/vol changes for each day. You can use daily sigmas, or whatever. The key is to know what you stand to make or lose at any given price/time/vol.
There are much 'cleaner' ways to do this assuming if all you want is delta exposure rather than being just long a single call option (e.g. synthetic forward will give you a delta of 1, gamma and vega neutral). What you essentially want is a position where your vega exposure isn't too high (i.e. longer expiry), but also where you're not going to suffer from theta losses. Another thing worth noting is that your gamma exposure will be highest at the money closer to expiration.
A more easy way is this simulator software I use www.tradoroptions.com It has "Market simulations" that does exatly that, so I can clearly see time decay theta.