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Option Pricing using Quantum Computers
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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.
Forward citations
Cited by 4 Pith papers
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On the encoding complexity of quantum numerical integration: an angle-structure characterization
Low-degree multilinear angle maps enable O(ε^{-1} log(1/ε)) quantum gate complexity for numerical integration on [0,1], with unconditional separations from classical quadrature for certain low-regularity functions.
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On the encoding complexity of quantum numerical integration: an angle-structure characterization
The encoding cost of quantum numerical integration is controlled by the multilinear degree of the amplitude angle map, yielding an O(ε⁻¹ log(1/ε)) gate count for affine encodings.
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Quantum Derivative Pricing for SPDEs via BDSDE Representation
Quantum-accelerated MLMC methods for BDSDE-based SPDE derivative pricing and Greeks achieve sampling complexity improvement from O(ε^{-2}) to O(ε^{-1}).
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Credit Risk Analysis using Quantum Computers
Quantum amplitude estimation algorithm for credit risk economic capital with qubit and runtime estimates on assumed future hardware.
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