Quantum pricing with a smile: implementation of local volatility model on quantum computer

Kaneko, Kazuya; Miyamoto, Koichi; Takeda, Norio; Yoshino, Kazuyoshi

doi:10.1140/epjqt/s40507-022-00125-2

Cited by 18 publications

(8 citation statements)

References 40 publications

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“…More recently, an approximate method to implement the Grover-Rudolph algorithm for standard normal probability distributions was presented in [29], where the authors suggest the expression in Eq. (B4), written as…”

Section: Algorithm A2 Tarf Examplementioning

confidence: 99%

A Threshold for Quantum Advantage in Derivative Pricing

Chakrabarti,

Krishnakumar,

Mazzola

et al. 2020

Preprint

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We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing -the re-parameterization method -that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 7.5k logical qubits and a T-depth of 46 million. We estimate that quantum advantage would require a executing this program at the order of a second. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.

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Section: Algorithm A2 Tarf Examplementioning

confidence: 99%

A Threshold for Quantum Advantage in Derivative Pricing

Chakrabarti,

Krishnakumar,

Mazzola

et al. 2020

Preprint

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“…It is known that a quadratic quantum speed-up in MCI is available [2] by calling quantum amplitude estimation (QAE) [3] as a sub-routine. Such is the ubiquity of Monte Carlo methods throughout the physical, biological, data and information sciences, that this has, in turn, spawned a great deal of interest in quantum Monte Carlo integration (QMCI) -most notably in applications related to finance such as option pricing [4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth

Herbert

2022

Quantum

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This paper proposes a method of quantum Monte Carlo integration that retains the full quadratic quantum advantage, without requiring any arithmetic or quantum phase estimation to be performed on the quantum computer. No previous proposal for quantum Monte Carlo integration has achieved all of these at once. The heart of the proposed method is a Fourier series decomposition of the sum that approximates the expectation in Monte Carlo integration, with each component then estimated individually using quantum amplitude estimation. The main result is presented as theoretical statement of asymptotic advantage, and numerical results are also included to illustrate the practical benefits of the proposed method. The method presented in this paper is the subject of a patent application [Quantum Computing System and Method: Patent application GB2102902.0 and SE2130060-3].

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“…Some implementations for this type of oracle have been proposed. Originally, the implementation as a series of arithmetic circuits and controlled rotation was proposed in [53], and some extensions and modifications on this have been also proposed recently [54][55][56]. In another direction, some state preparation methods based on variational algorithms with parametric quantum circuits have been considered [57][58][59][60][61].…”

Section: Definitionmentioning

confidence: 99%

Quantum algorithm for calculating risk contributions in a credit portfolio

Miyamoto

2022

EPJ Quantum Technol.

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Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have been proposed. In this paper, we focus on another problem in credit risk management, calculation of risk contributions, which quantify the concentration of the risk on subgroups in the portfolio. Based on the recent quantum algorithm for simultaneous estimation of multiple expected values, we propose the method for credit risk contribution calculation. We also evaluate the query complexity of the proposed method and see that it scales as $\widetilde{O} (\sqrt{N_{\mathrm{gr}}}/\epsilon )$ O ˜ ( N gr / ϵ ) on the subgroup number $N_{\mathrm{gr}}$ N gr and the accuracy ϵ, in contrast with the classical method with $\widetilde{O} (\log(N_{\mathrm{gr}})/\epsilon^{2} )$ O ˜ ( log ( N gr ) / ϵ 2 ) complexity. This means that, for calculation of risk contributions of finely divided subgroups, the advantage of the quantum method is reduced compared with risk measure calculation for the entire portfolio. Nevertheless, the quantum method can be advantageous in high-accuracy calculation, and in fact yield less complexity than the classical method in some practically plausible setting.

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Quantum pricing with a smile: implementation of local volatility model on quantum computer

Cited by 18 publications

References 40 publications

A Threshold for Quantum Advantage in Derivative Pricing

A Threshold for Quantum Advantage in Derivative Pricing

Quantum Monte Carlo Integration: The Full Advantage in Minimal Circuit Depth

Quantum algorithm for calculating risk contributions in a credit portfolio

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