Paper: arXiv 2303.09682

Authors: Titos Matsakos, Stuart Nield

Abstract

Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. If a probability distribution is available, Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up in measuring its properties as compared to their classical counterparts. Recent studies have explored the calculation of common risk measures and the optimisation of QAE algorithms by initialising the input quantum states with pre-computed probability distributions. If such distributions are not available in closed form, however, they need to be generated numerically, and the associated computational cost may limit the quantum advantage. In this paper, we bypass this challenge by incorporating scenario generation – i.e. simulation of the risk factor evolution over time to generate probability distributions – into the quantum computation; we refer to this process as Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that implement stochastic models for equity (geometric Brownian motion), interest rate (mean-reversion models), and credit (structural, reduced-form, and rating migration credit models) risk factors. We then integrate these models with QAE to provide end-to-end examples for both market and credit risk use cases.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents an innovative end-to-end framework for Quantum Monte Carlo simulations by directly incorporating stochastic scenario generation into quantum circuits using Quantum Amplitude Estimation. While mathematically sophisticated and novel in its quantum circuit construction across equity, rate, and credit models, it lacks extensive empirical backtesting and real-world market validation, leaning heavily on theoretical and simulation-based proofs of concept.

Research Flowchart

  flowchart TD
    A["Research Goal: Integrate scenario generation into QMC for end-to-end financial risk analytics"] --> B["Inputs: Stochastic Models for Equity, Interest Rates, & Credit Risk"]
    B --> C["Construct Quantum Circuits for Risk Factor Evolution (SDEs & Credit Models)"]
    C --> D["Integrate Circuit Outputs with Quantum Amplitude Estimation (QAE)"]
    D --> E["Execute End-to-End Quantum Monte Carlo Simulations"]
    E --> F["Outcomes: Bypasses closed-form limits & achieves quadratic speed-up for VaR/pricing"]