Option Pricing using Quantum Computers (1905.02666v5)

Abstract: We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

• The paper demonstrates that amplitude estimation on quantum circuits yields a quadratic speedup for pricing complex derivatives.
• It details efficient quantum circuit designs optimized for various option types including European, basket, Asian, and barrier options.
• The study employs error mitigation strategies such as Richardson extrapolation to enhance reliability on current quantum hardware.

Analysis of Option Pricing Using Quantum Computers

The paper "Option Pricing using Quantum Computers" presents a comprehensive methodology for pricing financial options via quantum computing, employing amplitude estimation to achieve significant computational speedups over classical methods. The investigation focuses on implementing option pricing models using gate-based quantum computers, addressing complex derivatives such as vanilla, multi-asset, and path-dependent options like barrier options.

The methodology focuses primarily on leveraging amplitude estimation (AE), a quantum algorithm that provides a quadratic speedup over classical Monte Carlo simulations. The applicability of AE is demonstrated across various option types: European, basket, Asian, and barrier, each presenting unique challenges in their respective payoff computations.

Key Technical Contributions

1. Quantum Circuit Design: Central to the methodology is the implementation of quantum circuits that leverage AE. The authors detail the circuit construction for initializing probability distributions, computing option payoffs, and employing quantum algorithms to determine the expected payoff. The circuits are optimized for the nuances of each option type, ensuring efficient state preparation and transformation on quantum hardware.
2. Amplitude Estimation (AE) without Phase Estimation: The adaptation of AE to circumvent the need for phase estimation significantly reduces the resource requirements, allowing potential operation on available quantum devices. This adaptation is crucial given the current limitations in quantum hardware fidelity and coherence times.
3. Error Mitigation Techniques: Given intrinsic quantum noise and errors, the employment of error mitigation strategies is pivotal. The authors implement a simple yet effective error mitigation scheme, notably Richardson extrapolation, which contributes to enhancing the robustness of quantum operations.

Practical Implications

The quantum approach to option pricing proposes consequential impacts on the finance industry where high computational demand persists due to the complexity and volume of derivative contracts. Quantum computing's ability to address multi-dimensional integrals and stochastic processes more efficiently than classical analogs could revolutionize risk assessment and trading strategies. The paper provides a clear indication of substantial reductions in computational time and resources, factors critical in high-frequency trading and portfolio management.

Future Directions

Given its promising numerical results, the paper suggests several avenues for further exploration:

• Expansion of Financial Applications: The methodology could be explored beyond option pricing to include other derivatives and risk management computations.
• Improvement in Quantum Algorithms: Further optimizing AE and integrating more sophisticated error mitigation techniques may expand applicability to larger and more complex financial instruments.
• Hybrid Quantum-Classical Systems: Development of hybrid models that combine quantum strengths in handling complexity with classical methods for tasks more suited to traditional computation could yield more pragmatic and scalable solutions.

While the work demonstrates a solid foundational step towards practical quantum finance solutions, it signals the necessity for parallel advancements in quantum hardware to fully realize the theoretical benefits proposed. The convergence of quantum computing and financial engineering holds the potential to deliver unprecedented insights and efficiencies in financial markets.