Quantum Risk Analysis of Financial Derivatives
arxiv(2024)
摘要
We introduce two quantum algorithms to compute the Value at Risk (VaR) and
Conditional Value at Risk (CVaR) of financial derivatives using quantum
computers: the first by applying existing ideas from quantum risk analysis to
derivative pricing, and the second based on a novel approach using Quantum
Signal Processing (QSP). Previous work in the literature has shown that quantum
advantage is possible in the context of individual derivative pricing and that
advantage can be leveraged in a straightforward manner in the estimation of the
VaR and CVaR. The algorithms we introduce in this work aim to provide an
additional advantage by encoding the derivative price over multiple market
scenarios in superposition and computing the desired values by applying
appropriate transformations to the quantum system. We perform complexity and
error analysis of both algorithms, and show that while the two algorithms have
the same asymptotic scaling the QSP-based approach requires significantly fewer
quantum resources for the same target accuracy. Additionally, by numerically
simulating both quantum and classical VaR algorithms, we demonstrate that the
quantum algorithm can extract additional advantage from a quantum computer
compared to individual derivative pricing. Specifically, we show that under
certain conditions VaR estimation can lower the latest published estimates of
the logical clock rate required for quantum advantage in derivative pricing by
up to ∼ 30x. In light of these results, we are encouraged that our
formulation of derivative pricing in the QSP framework may be further leveraged
for quantum advantage in other relevant financial applications, and that
quantum computers could be harnessed more efficiently by considering problems
in the financial sector at a higher level.
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