Suppose I'm looking at an options chain on my screen and I've decided whether or not I want a put or a call, but I haven't decided what strike is best. Additionally, I have a price target in my head and for whatever reason I think the stock will be priced at X on or before day Y. I want to decide which strike will give me the largest return if I'm right, but I also want to minimize my loss in case I'm wrong.
Is there a mathematical model for this? Obviously Black Scholes is involved but there are too many variables that it's difficult to visualize. And I also know zilch about quantitative finance (although I do have a degree in math so if someone points me in the right direction I should be good). I can sit there and punch in 800 different scenarios into a calculator but obviously with a rapidly changing price you don't always have time for this.
One thing that might be helpful is if there was a tool that would let you specify all but 1 (or 2) variable(s) of Black Scholes and then show you a 2D (or 3D) graph of the function as your variable varies. For example, let's say I want to see what happens if I keep # of days to expiration and market price the same, but vary strike price. It should show some kind of 2D graph that might help me make a decision if I feel confident that the price will be X at some point on a certain day (maybe I feel like an equity is going to test some key support point, for example). Or perhaps I want to see what happens if I vary both market value and # of days to expiration but leave strike the same. This might help me decide what would happen with a given option if I'm wrong and I let it ride too long, for example.
It seems like somewhere in here there's a numerical integration waiting to happen that I could supply a list of "probabilities" that I think represent how likely the underlying is to reach certain prices on different days during the contract period, and it would just spit out an "expected profit value" for each strike price making it a trivial decision which strike to choose.
Am I making sense here? Is there any kind of tool that helps with this? Is there a more practical approach to choosing the best strike price to get in on something at? (Even if there is a more practical approach, I'm still curious if anyone can enlighten me about a theoretical approach).