How to Profit from Mispriced Options
Many traders do not know this, but if one looks at the profit/loss (P&L) chart of a covered call and a cash-secured put on the same strike, they are borderline identical (save any differences in margin use). This is proven in a formula called put-call parity.
Put-call parity is kind of like the duct tape of the options world; it holds the entire options universe together. No matter how complex the model is in the programmed trade, if this simple formula isn't taken into account, the complex model is likely to cause its operator a lot of problems.
Put-call parity proves that if a call is trading at a given price, then the put has a direct quantifiable value that the trader can calculate. The formula for put-call parity is:
C-P = S-X + (I-D)
C = call
P = put
S = Stock
X = Strike
I = Interest
D = Dividends
This likely sounds crazy in the day and age of computers, but up until about 2003, floor traders spent a majority of their floor time looking up at the option screens and converting calls into puts and vice versa. If the trader found a call or a put that was mispriced, the trader would then trade that option. The idea was the trader was trying to lock in "edge." "Edge" is a term professional traders use for the value the trader enters an option trade above or below its theoretical value.
Here is an example. Suppose stock XYZ is trading at $56, the April 55 call is trading at $4, there is 5 cents in interest to collect (we are pretending rates are a lot higher than they currently are), and the stock has a 25-cent dividend between today and expiration.