If a year ago a company issued stock options at a $5 exercise price per share, but today they issued them at a $2.50 exercise price per share, does that mean the company has been de-valued by 50%, or is there no correlation between what a company is valued at and the exercise price?
There could also be some degree of dilution at play here. If they are rapidly expanding and hiring, or if they took on another round of funding each share may have a lower amount of value though the company might be worth more than they were previously. The newly issued options may also be of a different class.
I'm guessing you're talking about options given to employees. The company can issue stock options at whatever strike price it wants. The difference between the strike price and the actual market value is considered income to the employee. You can get the options at $0 strike just as well (although companies generally just give RSUs instead in this case).
There are a LOT of variables at play here, so with the info you've provided we can't give you an exact answer. Generally speaking, employee options at a startup are valued by a 409a valuation (http://en.wikipedia.org/wiki/Internal_Revenue_Code_section_409A) once a year or more often. But it's entirely possible that the company split its shares, or took a round of funding that reduced their valuation, or any other number of things. We'd need a good bit more information (which you may or may not have) to really answer the question.
1I assume you mean the company shares were split... Rather than the company was split, although also valid.– AronOct 23, 2018 at 15:53