[mehrdada]

You have to standardize on some common granularity for strikes/expiration dates so that each symbol has sufficient volume so that the market would not get too sparse. The theory does not require it, but when you are building an exchange, I suppose that'd be of a practical concern to you. You want interchangeability in derivative contracts and don't want each individual contract to be a snowflake.

There are "mini" options that control 10 shares, for example, but they usually have higher bid-ask spread reflecting the higher cost of pricing accurately/transaction fee/lower liquidity.

[km3r]

Wouldn't make more sense to make contracts that control 1 share so that sparseness is minimized?

[betterunix2]

You would have contracts trading for less than a dollar, which would make the system a lot less efficient (higher transaction fees etc.), not to mention raising the computational cost of matching contracts when they are exercised (there would be far more contracts to deal with).