Lets see how an option might be constructed and valued with the four coin toss model. Your friend says hed like to bet so that he only wins! (Dont we all?) He really hates paying when he loses, but he wouldnt be against paying a little something up front before the game starts. If he loses, you keep his up-front money. If he wins, he gets paid appropriately.
Is there some small amount he can pay you before the tossing starts and not be liable for paying any more regardless of outcome, but if his ship comes in (he wants the long shot again, exactly four heads) he will collect exactly $1?
We can accommodate him, and you are probably already figuring out how. It turns out his request is identical to a simple option. This is the same long-shot bet we reviewed in Variation 1 of the four coin toss game. There are 15 paths against, with 1 path for. Said another way, for every 16 games your friend will win 1 and lose 15. So he must pay $1/16 before each game begins. After 16 games (on average), he will win $1 from you, but he will have prepaid $1/16 multiplied by 16 which equals $1. Therefore, he will be even, as will you. You just created your first option.
You must charge him a prepayment that equals his expected gain. This is it. This is what options are all about: The buyer must prepay what his expected gain is. This is the answer to every option valuation question you will ever have.
If you learn only one thing from our studies, learn this lesson: Every option formula you will ever run into is merely trying to compute the prepayment required to break even. Put another way, the option formulas are trying to calculate what the expected gain is and charge that amount up front.
If the option was free, your friend would never lose. Charging a fair price up front ensures that both you and your friend will break even over many, many trials. If you can figure out expected gain, you can easily price any option. (Notice that in our games everything takes place the same day, so there is no time delay in payment. Therefore, no discounting, present value, or interest rate factors enter this simplified picture. Unfortunately there is a need for these adjusting factors for real options.) There are many variations on the theme, however, and clever entrepreneurs are constantly revising the game strategies and outcome payoffs.
Your friend is not betting on a long shot anymore. That means if zero heads arrive, you must pay zero dollars. One head, you pay $1. Up through four heads wherein you pay $4. Obviously your friend never risks a thing, so he must pay something up front. But how much?
As our friends game designs change we must also change, but one principle always holds: He must pay us an amount identical to his expected gain (or our expected loss; its the same thing). That means that sometimes he wins, sometimes he loses, but over a very long time we both should break even. This is the theory as based on fair games, break-even payoffs, and probability distributions.
Binary options will definitely help you. In order to understand binary options better, read this article once more.