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arXiv:2303.06089

Real Option Pricing using Quantum Computers

Manzano, Alberto, Gonzalo A. Casanova Ferro, Álvaro Leitao, Carlos Vázquez, Gómez, Andrés

Published Mar 10, 2023• 0 citations
arXivHTMLPDF

Abstract

In this work we present an alternative methodology to the standard Quantum Accelerated Monte Carlo (QAMC) applied to derivatives pricing. Our pipeline benefits from the combination of a new encoding protocol, referred to as the direct encoding, and a amplitude estimation algorithm, the modified Real Quantum Amplitude Estimation (mRQAE) algorithm. On the one hand, the direct encoding prepares a quantum state which contains the information about the sign of the expected payoff. On the other hand, the mRQAE is able to read all the information contained in the quantum state. Although the procedure we describe is different from the standard one, the main building blocks are almost the same. Thus, all the extensive research that has been performed is still applicable. Moreover, we experimentally compare the performance of the proposed methodology against the standard QAMC employing a quantum emulator and show that we retain the speedups.

DOI
10.48550/arxiv.2303.06089

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Abstract In this work we present an alternative methodology to the standard Quantum Accelerated Monte Carlo (QAMC) applied to derivatives pricing. Our pipeline benefits from the combination of a new encoding protocol, referred to as the direct encoding, and an amplitude estimation algorithm, the modified Real Quantum Amplitude Estimation (mRQAE) algorithm. On the one hand, the direct encoding prepares a quantum state which contains the information about the sign of the expected payoff. On the other hand, the mRQAE is able to read all the information contained in the quantum state. Although the procedure we describe is different from the standard one, the main building blocks are almost the same. Thus, all the extensive research that has been performed is still applicable. Moreover, we experimentally compare the performance of the proposed methodology against the standard QAMC employing a quantum emulator and show that we retain the speedups.
This work introduces an end-to-end framework for multi-asset option pricing that combines market-consistent risk-neutral density recovery with quantum-accelerated numerical integration. We first calibrate arbitrage-free marginal distributions from European option quotes using the Normal Inverse Gaussian (NIG) model, leveraging its analytical tractability and ability to capture skewness and fat tails. Marginals are coupled via a Gaussian copula to construct joint distributions. To address the computational bottleneck of the high-dimensional integration required to solve the option pricing formula, we employ Quantum Accelerated Monte Carlo (QAMC) techniques based on Quantum Amplitude Estimation (QAE), achieving quadratic convergence improvements over classical Monte Carlo (CMC) methods. Theoretical results establish accuracy bounds and query complexity for both marginal density estimation (via cosine-series expansions) and multidimensional pricing. Empirical tests on liquid equity entities (Credit Agricole, AXA, Michelin) confirm high calibration accuracy and demonstrate that QAMC requires 10-100 times fewer queries than classical methods for comparable precision. This study provides a practical route to integrate arbitrage-aware modelling with quantum computing, highlighting implications for scalability and future extensions to complex derivatives.
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.
Option pricing is a fundamental problem in quantitative finance, where the accuracy and efficiency of valuation methods directly affect investment and risk management decisions. While the Black-Scholes model provides a closed-form solution for European options, numerical approaches such as Monte Carlo simulation are widely used when analytical methods are intractable. However, Monte Carlo suffers from slow convergence with complexity O(1/ε2).Quantum Amplitude Estimation (QAE), an algorithm in quantum computing, promises a quadratic speedup with complexity O(1/ε). This paper implements QAE, specifically Iterative Amplitude Estimation (IAE), for European call option pricing and compares its performance against Monte Carlo simulation and the Black-Scholes model. Experiments are conducted on both Qiskit simulators and IBM Quantum hardware (ibm_brisbane).Results show that QAE achieves estimates close to Monte Carlo and analytical benchmarks, with mean payoff deviations of less than 0.01. While QAE produces wider confidence intervals due to noise and discretization, the findings demonstrate its potential scalability advantage for future quantum finance applications.
This work presents a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant probability distributions can be prepared in quantum superposition, the payoff functions can be implemented via quantum circuits, and the price of financial derivatives can be extracted via quantum measurements. We show how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimate for the price with high confidence. This work provides a starting point for further research at the interface of quantum computing and finance.
The article provides a literature review and analysis of quantum computing methods in the context of option pricing, comparing them against a strict classical benchmark and recommending a viable way forward to quantum computing implementation. We assess the capabilities and the weaknesses of Windows-choice models closed-form legacy formulae of vanillas, lattice/PDE true hockeygoal models of early exercise, and Monte Carlo models of flexibleness and point out where classical run attracted and precision restraints are shown to apply in the new generation(s): complexity of variables, in this path dependence, in a portfolio composing. We proceed to describe quantum algorithms that are based on quantum Monte Carlo which is centered on amplitude-estimation-based algorithms to cut down on contact with sampling; avoiding the scale of classical Monte Carlo and are particularly appealing to complex derivatives; we describe circuit components to prepare states, encode payoffs, and approximate expectations. The study establishes research priorities that achieve scale implies: depth frequently used to design loaders in, and variants of payoff circuits, workflow standardizations that exchange the exchange of error-resilient quantum modules and technological risk engines in the NISQ age. In general, the paper offers a single source of information on classical-quantum option pricing, clean insertion architecture to deploy hybrids and a roadmap between demonstrations and reliable production.