Financial volatility prediction is currently one of the most demanding challenges in quantitative finance. The basic limitations in traditional classical machine learning methods are that they use fixed feature representations and deterministic similarity measures. The paper explores the potential of trainable quantum kernel methods as a principled alternative for binary volatility regime classification, based on the price data of Bitcoin (BTC-USD). A complete pipeline is suggested, using mutual information-based feature selection, a data re-uploading parameterized quantum circuit, and optimization of kernel-target alignment (KTA) via Adam optimizer. The system is compared to Long Short-Term Memory (LSTM) networks and radial basis function (RBF) SVMs on the same stratified evaluation subset. The LSTM has the best accuracy of 91.06 \% and AUC of 0.9732, but the trainable quantum kernel performs better than the untrained ablation baseline in all measures. When subjected to controlled Gaussian injection of noise, the quantum models retain and in some cases even enhance accuracy. The trainable quantum kernel is 80.8 \% accurate with just 14 samples in the low-data regime (25 percent training fraction), and even better than the RBF-SVM at 77.2 percent with 124 samples, highlighting the practical data efficiency of task-specific quantum feature maps.

Quantum kernel methods,quantum machine learning,financial volatility prediction,kernel-target alignment,support vector machine,Bitcoin,LSTM,parameterized quantum circuits