The growing complexity and velocity of derivatives markets demand risk management systems capable of processing massive, high-frequency data streams and responding to rapidly evolving exposures. This paper presents a critical review and conceptual framework for integrating Big Data analytics with distributed computing architectures to enable real-time risk management of derivatives portfolios. We analyze current practices in market and credit risk computation, highlighting limitations in traditional centralized infrastructures, including latency bottlenecks, computational inefficiencies, and delayed visibility into systemic risk signals. Emerging technologies — such as in-memory distributed clusters, event-driven streaming pipelines, and scalable machine learning models — are examined for their potential to accelerate valuation adjustments, margin calculations, and stress testing under volatile market conditions. We propose an architecture that leverages heterogeneous data sources, parallelized pricing engines, and continuous predictive analytics to support dynamic hedging decisions and regulatory compliance with near-zero latency. Key challenges, including data quality governance, model interpretability, cyber-resilience, and cost-to-performance trade-offs, are discussed to guide successful implementation. The synthesis underscores that a harmonized Big Data–distributed computing ecosystem can fundamentally enhance the accuracy, agility, and robustness of derivatives risk management — enabling financial institutions to mitigate emerging risks proactively while sustaining competitive advantage in increasingly digital capital markets.