Quantum computing promises new computational paradigms that may materially alter approaches to financial risk modelling and high-frequency trading (HFT). This paper examines the theoretical foundations and near-term prospects for quantum algorithms applied to core financial tasks: Monte Carlo-based derivative pricing and risk estimation, combinatorial and convex optimization for portfolio allocation, and latency-sensitive decision processes characteristic of HFT. We synthesize recent developments in quantum Monte Carlo methods, quantum-accelerated optimization (including quantum annealing and variational hybrid algorithms), and quantum-enhanced machine learning, assessing their algorithmic complexity, noise sensitivity, and integration pathways with classical infrastructure. Emphasis is placed on practical performance metrics—error bounds, time-to-solution under realistic device noise, and communication/latency constraints relevant to trading venues—and on regulatory, cryptographic, and operational risks introduced by quantum-capable systems. Case studies illustrate how hybrid quantum-classical workflows could improve risk estimation accuracy and portfolio rebalancing decisions, while identifying the principal bottlenecks that prevent immediate adoption in latency-constrained HFT environments. We conclude with a roadmap for translational research that prioritizes benchmarking, robustness to adversarial market behavior, and the development of quantum-resilient cryptographic practices for financial institutions