This paper presents two novel hybrid classical-quantum methods for pricing financial derivatives by leveraging Quantum Machine Learning (QML) models based on Parametrized Quantum Circuits (PQCs). The core idea is to approximate the probability distribution of the underlying asset (either its probability density function or cumulative distribution function) using truncated Fourier series, whose coefficients are learned from market data via PQC-based quantum models. The option price is then computed as a sum of products of Fourier coefficients from the payoff and the distribution, avoiding direct Monte Carlo simulation. The authors provide theoretical justification by invoking universal approximation theorems for PQCs, which guarantee convergence in various function spaces (C0, Lp, Hk). Numerical experiments compare the proposed methods against Quantum Accelerated Monte Carlo (QAMC) as a benchmark, analyzing the impact of data size and PQC dimensionality on accuracy and computational cost. Results show that the QML-based methods achieve remarkable accuracy, making them a competitive quantum alternative for derivative pricing, with the CDF-based formulation offering enhanced stability for discontinuous payoffs.