Quantum Computational Algorithms for Derivative Pricing and Credit Risk in a Regime Switching Economy

ArXiv ID: 2311.00825 “View on arXiv”

Authors: Unknown

Abstract

Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both realistic in terms of mimicking financial market risks as well as more amenable to potential quantum computational advantages. The type of models we study are based on a regime switching volatility model driven by a Markov chain with observable states. The basic model features a Geometric Brownian Motion with drift and volatility parameters determined by the finite states of a Markov chain. We study algorithms to estimate credit risk and option pricing on a gate-based quantum computer. These models bring us closer to realistic market settings, and therefore quantum computing closer the realm of practical applications.

Keywords: Regime Switching, Markov Chain, Quantum Computing, Credit Risk Estimation, Option Pricing, Derivatives/Credit

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats
  • Why: The paper is dense with advanced mathematical formalism including Markov chains, continuous-time stochastic processes, and quantum circuit derivations, but focuses on theoretical algorithm design with no backtested implementations or real data reported.
  flowchart TD
    A["Research Goal: Develop quantum algorithms for derivative pricing & credit risk in a regime-switching economy, addressing limitations of existing quantum approaches."] --> B["Methodology: 1. Construct Stochastic Model 2. Derive Quantum Algorithms"]
    B --> C["Key Model Inputs: <br>Regime-Switching Markov Chain<br>Geometric Brownian Motion (GBM)<br>Drift & Volatility Parameters per Regime"]
    C --> D["Computational Process: <br>Gate-based Quantum Algorithms<br>1. Monte Carlo Simulation<br>2. Amplitude Estimation<br>(Estimating Option Prices & Credit Risk)"]
    D --> E["Key Findings & Outcomes: <br>1. Validated model realism for financial markets<br>2. Demonstrated potential for quantum advantage<br>3. Algorithm designed for current NISQ hardware constraints<br>4. Brings quantum finance closer to practical applications"]