Yes, you are right. Stock options even before they are vested have values. Such values are computed using complicated option pricing models such as the Black-Scholes option pricing model. These models are based on several factors.
Changes in a company's stock price have no impact on the financial statements of that company. Remember that stock are traded in the stock exchange which is a secondary market, meaning transactions are between investors of stocks and NOT with the company. Hence, the company does not record any entry in its books reflecting the changes in its stock price. Therefore, the company does nothing.