Option Pricing using Quantum Computers
Nikitas Stamatopoulos,Daniel J. Egger,Yue Sun,Christa Zoufal,Christa Zoufal,Raban Iten,Raban Iten,Ning Shen,Stefan Woerner +8 more
TL;DR: 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.
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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.
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Citations
Quantum Computing for Finance: State-of-the-Art and Future Prospects
Daniel J. Egger,Claudio Gambella,Jakub Marecek,Scott McFaddin,Martin Mevissen,Rudy Raymond,Andrea Simonetto,Stefan Woerner,Elena Yndurain +8 more
- 13 Oct 2020
TL;DR: This article outlines the applicability, state-of-the-art, and potential of quantum computing for problems in finance, and describes in detail quantum algorithms for specific applications arising in financial services, such as those involving simulation, optimization, and machine learning problems.
Warm-starting quantum optimization
TL;DR: Results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth, and it is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.
Iterative quantum amplitude estimation
Dmitry Grinko,Dmitry Grinko,Dmitry Grinko,Julien Gacon,Julien Gacon,Christa Zoufal,Christa Zoufal,Stefan Woerner +7 more
TL;DR: In this paper, a variant of Quantum Amplitude Estimation (QAE) called Iterative QAE (IQAE) is introduced, which does not rely on Quantum Phase Estimation and is only based on Grover's Algorithm, which reduces the required number of qubits and gates.
Grover Adaptive Search for Constrained Polynomial Binary Optimization
TL;DR: This work develops a way to construct efficient oracles to solve CPBO problems using GAS algorithms and demonstrates the potential speed-up for the portfolio optimization problem, i.e. a QUBO, using simulation.
Quantum computing for finance
Dylan Herman,Cody Googin,Xiaoyuan Liu,Yue Sun,Alexey Galda,Ilya Safro,Marco Pistoia,Yuri Alexeev +7 more
TL;DR: The classical techniques used by the financial industry is outlined and the potential advantages and limitations of quantum techniques are discussed, as well as challenges that physicists could help tackle.
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