Quantum Risk Analysis of Financial Derivatives

• DOI: 10.48550/arxiv.2404.10088
• Publication Date: 2024-04-15
• Authors: Nikitas Stamatopo...; B. D. Clader; Stefan Woerner; William J. Zeng
• Keywords: FOS: Economics and business; Quantum Physics; Quantitative Finance - Computational Finance; FOS: Physical sciences; Computational Finance (q-fin.CP); Quantum Physics (quant-ph)

We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional (CVaR) of financial derivatives using computers: first by applying existing ideas from risk analysis derivative pricing, second based on a novel approach Quantum Signal Processing (QSP). Previous work in literature has shown that advantage is possible context individual pricing can be leveraged straightforward manner estimation VaR CVaR. The we this aim provide an additional encoding price over multiple market scenarios superposition computing desired values appropriate transformations system. perform complexity error both algorithms, show while have same asymptotic scaling QSP-based requires significantly fewer resources for target accuracy. Additionally, numerically simulating classical demonstrate algorithm extract computer compared pricing. Specifically, under certain conditions lower latest published estimates logical clock rate required up $\sim 30$x. In light these results, are encouraged our formulation QSP framework may further other relevant applications, computers could harnessed more efficiently considering problems sector higher level.