Which aspect is essential for achieving put-call parity?

Achieving put-call parity is fundamentally based on the requirement for both options to have the same expiration date and strike price. This principle ensures that the options can be effectively compared in terms of their intrinsic value and time value.

In essence, put-call parity reflects a theoretical relationship between the price of European call and put options with the same strike price and expiration date. If these parameters are not aligned, the options could yield different payoffs and thus be mispriced in the market. The coherence in expiration and strike price is crucial to maintain parity, ensuring that the combined position of a call option and a put option relative to an underlying asset hedges the same payoff regardless of how the underlying asset moves.

The other aspects mentioned, such as identical interest rates, equal likelihood of price changes, or the absence of market fluctuations, while they may influence the pricing of options in general, do not directly underpin the principle of put-call parity. This crucial relationship is solely dependent on the matching characteristics of the options involved.