Accurately estimating expected payoffs is central to the pricing of European call options, especially when valuation depends on low-probability events in the distribution tail. This study evaluates the performance of Quantum Amplitude Estimation (QAE), using Iterative Amplitude Estimation (IAE) and Maximum Likelihood Amplitude Estimation (MLAE), in pricing European call options based on historical Apple market data. Despite the theoretical advantages of QAE, our experiments show that both quantum estimators return an expected payoff of zero, even in scenarios where classical methods, Black-Scholes and Monte Carlo simulation yield significantly positive values. This outcome stems from the limited resolution imposed by limited uncertainty qubits, which inadequately encode small-amplitude, in-the-money price regions. While QAE circuits correctly identify the realized market outcome, they fail to capture the full expectation implied by the distribution. These results highlight the current limitations of QAE under realistic constraints and underscore the importance of enhanced encoding strategies for future quantum financial applications.