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In this paper, we introduce an efficient and end-to-end quantum algorithm tailored for computing the Value-at-Risk (VaR) and conditional Value-at-Risk (CVar) for a portfolio of European options. Our focus is on leveraging quantum computation to overcome the challenges posed by high dimensionality in VaR and CVaR estimation. While our innovative quantum algorithm is designed primarily for estimating portfolio VaR and CVaR for European options, we also investigate the feasibility of applying a similar quantum approach to price American options. Our analysis reveals a quantum 'no-go' theorem within the current algorithm, highlighting its limitation in pricing American options. Our results indicate the necessity of investigating alternative strategies to resolve the complementarity challenge in pricing American options in future research.
Wu et al. (Sat,) studied this question.