Which factor is critical in determining the price of an option?

The critical factor in determining the price of an option is the time remaining until expiration and the underlying asset's volatility. The time to expiration is important because the longer an option has until it expires, the more time there is for the underlying asset's price to move favorably. This can increase the option's potential value.

Additionally, the volatility of the underlying asset plays a significant role; higher volatility means a greater chance that the asset's price will fluctuate significantly, which in turn increases the likelihood of an option finishing in-the-money. Traders are willing to pay a premium for options associated with highly volatile assets because the potential for profit is greater. Thus, these two components—time until expiration and volatility—are foundational in options pricing models, such as the Black-Scholes model, which assesses the fair market value of options.

Other factors, while they can influence the market environment, do not have the same direct and immediate effect on option pricing as the time and volatility do. For instance, while the demand and supply dynamics can influence price in the short term, it's the intrinsic characteristics of time and volatility that fundamentally govern option pricing principles.