Much of option trading has its roots in game theory so let’s play a game.
I have a die and I will pay you $1.00 for every dot that shows up. You roll, a four, you get $4.00. Simple, right? What would you pay to play this game? If I wanted to be the one to roll, what would you make me pay?
Well, we can calculate the expected value of a proposition. Then, from there we can see how much “edge” (price entered away from expected value). So, the probability of rolling any number is the same, 1 out of 6. So we use our expected value formula to calculate: (1/6*1)+(1/6*2)+(1/6*3)+(1/6*4)+(1/6*5)+(1/6*6)=21/6 or 3.50. So, 3.5 is fair value.
THE LIQUIDITY FACTOR
Here’s where liquidity comes in. If we were to play this game once, I would need more “edge” to play because I only have one chance to be right. Who knows how much edge that is? For me, I would need one dollar of edge. So, my market would be $2.50/4.50. This is what market makers do every day.
If we were going to play this game one billion times, I would make my market 3.49/3.51. The liquidity is such that I am willing to take less in “edge” because I get to play so many times. If I play once I can only expect to make $1.
If I play one billion times I can expected to make ten million dollars! You see the same thing when trading stocks. Look at the market width in Facebook compared to a stock that trades very rarely. Facebook options will be a couple of pennies wide where the non-liquid stock will have markets that are orders of magnitude wider. Why? Because you don’t get to “roll the dice” as many times.
