Quantum Risk Analysis of Financial Derivatives

ArXiv ID: 2404.10088 “View on arXiv”

Authors: Unknown

Abstract

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 $\sim 30$x. 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.

Keywords: Value at Risk, Conditional Value at Risk, quantum algorithms, Quantum Signal Processing, derivative hedging

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper introduces advanced quantum algorithms (QAE, QSP) with significant mathematical derivations, including complexity analysis and error bounds. However, the empirical evidence is based on numerical simulations rather than real backtests or datasets, with a focus on theoretical resource estimates rather than implementation-heavy validation.
  flowchart TD
    A["Research Goal: <br>Estimate VaR/CVaR for Derivatives<br>using Quantum Advantage"] --> B["Method 1: Existing Quantum Risk Analysis<br>Applied to Derivatives"]
    A --> C["Method 2: Novel Approach<br>using Quantum Signal Processing QSP"]
    
    B & C --> D["Computational Process:<br>Encoding Prices & Market Scenarios<br>in Quantum Superposition"]
    
    D --> E["Data Inputs:<br>Derivative Pricing Models &<br>Market Scenario Simulations"]
    
    E --> F["Complexity &<br>Error Analysis"]
    
    F --> G["Key Outcomes: <br>1. QSP requires significantly fewer resources<br>2. 30x lower logical clock rate for advantage<br>3. Formulation extends to other financial apps"]