A company has 100,000 shares and 100,000 unexercised call options (company issued). Share price and strike price both at $1.
What country is this related to? I ask because, in the US, most people I know associate a "call" option with the instrument that is equivalent to 100 shares. So 100,000 calls would be 10,000,000 shares, which exceeds the number of shares you're saying the company has.
I don't know if that means you pulled the numbers out of thin air, or whether it means you're thinking of a different type of option? Perhaps you meant incentive stock options meant to be given to employees? Each one of those is equivalent to a single share. They just aren't called "call options".
In the rest of my answer, I'm going to assume you meant stock options.
I assume the fact that these options exist will slow any price increases on the underlying shares due to potential dilution?
I don't think the company can just create stock options without creating the underlying shares in the first place. Said another way, a more likely scenario is that company creates 200,000 shares and agrees to float 50% of them while reserving the other 50% as the pool for incentive employee stock. They then choose to give the employees options on the stock in the incentive pool, rather than outright grants of the stock, for various reasons. (One of which is being nice to the employees in regards to taxes since there is no US tax due at grant time if the strike price is the current price of the underlying stock.)
An alternative scenario when the company shares are liquidly traded is that the company simply plans to buy back shares from the market in order to give employees their shares when options are exercised. In this case, the company needs the cash on hand, or cash flow to take money from, to buy those shares at current prices.
Anyway, in either case, there is no dilution happening WHEN the options get exercised. Any dilution happened before or at the time the options were created. Meaning, the total number of shares in the company was already pre-set at an earlier time. As a result, the fact that the options exist in themselves will not slow price changes on the stock.
However, price changes will be impacted by the total float of shares in the company, or the impact to cash flow if the company has to buy shares to redeem its option commitments. This is almost the same thing you're asking about, but it is technically different as to timing.
If this is the case, can this be factored into any option pricing models like black-scholes?
You're including the effect just by considering the total float of shares and net profits from cash flow when doing your modelling.