Final answer:
The premium does influence whether the option holder exercises an option or not.
Step-by-step explanation:
Yes, the premium does influence whether the option holder exercises an option or not. The premium is the price that an option buyer pays to the option seller for the right to buy or sell the underlying asset at a specific price within a specified period of time. If the premium is high, it may make the option expensive and the option holder may choose not to exercise it. Conversely, if the premium is low, the option holder may be more inclined to exercise the option.