So knowing the concept of expected value and fair price of a bet, we can start diving into pricing an option. As a quick reminder: options are contracts that give you the right but not the obligation to buy/sell the underlying at a predetermined price (known as the strike price) on or before the expiration date. A call option will give you the right to buy and a put option will give you the right to sell.
We're not going to go into the mathematics of actually pricing an option (believe me, its complicated). Instead, we will look at the variables that are the input. In other words, we are going to look at the variables that change the expected value of outcome.
So, what variables might change the price of an option? Let's try to see what they are by looking at the definition of an option.
- Call or Put? The option will give you the right to buy or sell, so one of the variable must be: is this option a call or a put?
- Strike Price? Surely the price will change dramatically if I were comparing an option that gave me the right to buy something for $1 compared to the option that gave me the right to buy something for $40.
- Expiration Date? Another way to ask the question is, how much time is left between now (when I purchase/sell the option) until the expiration date?
There are three more that are not explicitly stated in the definition:
- Value of Underlying? This variable is a bit obvious. The right to buy corn for $4.00 a bushel would be valued differently if corn was trading at $4.50 compared to trading at $1.20.
- Risk Free Interest Rate? Since we are dealing with values in the future, we have to discount by the risk free interest rate. When I was trading (and even now) the risk-free interest rate is very close to zero. So, we won't talk about this too much.
- Volatility? This variable is not easy to understand. Basically, its asking how volatile your underlying is. Does it have an expected move of 3% each day or 0.3% each day? This variable makes a lot of sense if you think about the extremes. If there was a right to buy a $5 bill for $6, no one would purchase it because the price of a $5 bill is always $5 (i.e. volatility is zero). On the other extreme, if we have a stock that moved about erratically (i.e. high volatility), a right to purchase it at a higher price is attractive
With all these variables, we can specify which option we are talking about and estimate what the theoretical value of an option is. Using the theoretical value (the expected payout), if we buy it for cheaper than that and/or sell it for more than that, we are making a theoretical profit!