Open Interest (not Option Interest) represents the number of contracts that exist on any given day.
In order for a trade to occur, there must be a buyer and a seller. Each party may be opening or closing the contract. There are 4 scenarios:
Buy to Open (BTO) and Sell To Open (STO)
- Both parties are initiating a new position (one new buyer and one new seller) so open interest increases by one
BTO and Sell To Close (STC)
- If a contract owner sells to a new trader, open interest does not change (an existing contract is changing hands)
Buy To Close (BTC) and STO
- If someone short a contract buys from a new writer, open interest does not change (an existing contract is changing hands)
BTC and STC
- Both parties are closing an existing position (one previous buyer and one previous seller) so open interest declines by one
A call buyer is bullish. If that call purchase is to hedge a short position in the underlying, the trader is actually bearish. Therefore, there's no way to infer what an investor's directional bias is from call (or put) purchases and possible changes in open interest. To that end, some delve into combining price, volume and open interest to determine direction. I've never been able to discern it but here's an article from Investopedia that explains it.
In general, option pricing follows stock price. Stock price can follow option price but those are nuanced exceptions and tend to have little to no effect on share price unless it's a very illiquid stock.
For example, if option pricing strays from put/call parity, a market maker or floor trader will execute a conversion or a reversal which leads to buying or selling of shares to drive option prices back in line.
Another example might be if a option owner exercises a large amount of options and the counter party(ies) have naked options and must cover the assignment. These are infrequent exceptions and they occur randomly.