Evaluating Quantum Amplitude Estimation for Pricing Multi-Asset Basket Options

Accurate and efficient pricing of multi-asset basket options poses a significant challenge, especially when dealing with complex real-world data. In this work, we investigate the role of quantum-enhanced uncertainty modeling in financial pricing options on real-world data. Specifically, we use quantum amplitude estimation and analyze the impact of varying the number of uncertainty qubits while keeping the number of assets fixed, as well as the impact of varying the number of assets while keeping the number of uncertainty qubits fixed. To provide a comprehensive evaluation, we establish and validate a hybrid quantum-classical comparison framework, benchmarking quantum approaches against classical Monte Carlo simulations and Black-Scholes methods. Beyond simply computing option prices, we emphasize the trade-off between accuracy and computational resources, offering insights into the potential advantages and limitations of quantum approaches for different problem scales. Our results contribute to understanding the feasibility of quantum methods in finance and guide the optimal allocation of quantum resources in hybrid quantum-classical workflows.

💡 Research Summary

This paper investigates the practical use of Quantum Amplitude Estimation (QAE) for pricing multi‑asset basket options on real‑world market data. The authors first collect daily adjusted close prices for a set of equities (e.g., AAPL, GOOG, MSFT) over the period January 1 – June 30 2024 using the yfinance library. Log‑returns are computed, and per‑asset mean and volatility are estimated, then scaled to the option’s maturity. These statistical parameters are used to construct discrete probability distributions for each asset, which are encoded onto “uncertainty qubits.” If n qubits are allocated per asset, the price space is discretized into 2ⁿ points; for d assets the total register requires d·n qubits plus one objective qubit that flags whether the basket payoff exceeds the strike.

The QAE routine prepares the joint distribution state, applies a Grover‑type amplitude‑amplification operator repeatedly, and extracts the target amplitude p = sin²θ via quantum phase estimation (or its iterative variant). Two systematic studies are performed: (1) fixing the number of assets while varying the number of uncertainty qubits (1–4), and (2) fixing the qubit count while increasing the number of assets (2–5). The first study shows that adding qubits refines the price grid, dramatically reducing estimation error but at the cost of exponential growth in circuit depth and gate count. The second study reveals that as the basket dimension grows, encoding realistic cross‑asset correlations becomes increasingly resource‑intensive; with limited qubits the correlation structure is approximated poorly, leading to bias in the estimated option price.

Quantum results are benchmarked against classical Monte Carlo simulations (with large sample sizes) and Black‑Scholes calculations (single‑asset closed form). While QAE theoretically offers a quadratic speed‑up—requiring O(1/ε) quantum samples versus O(1/ε²) classical samples for a target precision ε—actual hardware constraints (gate errors, decoherence, limited qubit counts) diminish this advantage. With only 1–2 uncertainty qubits the price grid is too coarse, producing sizable absolute errors; with 3–4 qubits the error drops substantially but circuit depths of 50–100 gates exceed current NISQ coherence times.

The authors conclude that a careful balance between quantum resources (qubit number, circuit depth) and problem size (asset dimensionality) is essential. Their hybrid quantum‑classical workflow, which integrates real market data, provides a concrete benchmark for future quantum finance research. They suggest that advances in error mitigation, more efficient state‑loading techniques, and iterative amplitude‑estimation variants could bridge the gap, eventually enabling quantum‑enhanced pricing for realistic, high‑dimensional portfolios.