Quantum computation for pricing the collateralized debt obligations

Tang, Hao; Pal, Anurag; Qiao, Lu-Feng; Wang, Tianyu; Gao, Jun; Jin, Xian-Min

doi:10.1002/que2.84

Cited by 21 publications

(17 citation statements)

References 34 publications

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“…Tang et al [318] presented quantum procedures for both the P l and P f operators used for quantum Monte Carlo integration. The goal was to utilize QAE to estimate the expected loss of a given tranche.…”

Section: Collateralized Debt Obligationsmentioning

confidence: 99%

“…The equity tranche is the first to bear loss; the mezzanine tranche investors bear loss if the loss is greater than the first attachment point; and the senior tranche investors lose money if the loss is greater than the second attachment point. Although the senior tranche is protected from loss, other default events can cause the CDO to collapse, such as events that caused the 2008 financial crisis [318].…”

Section: Collateralized Debt Obligationsmentioning

confidence: 99%

See 1 more Smart Citation

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

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Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

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Section: Collateralized Debt Obligationsmentioning

confidence: 99%

Section: Collateralized Debt Obligationsmentioning

confidence: 99%

A Survey of Quantum Computing for Finance

Herman¹,

Googin²,

Liu³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In recent years, applications of quantum computers have been discussed in financial engineering. Specifically, the applications include portfolio optimization [1-3], risk measurement [4][5][6][7][8], and derivative pricing [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Comprehensive reviews of these topics are presented in Refs.…”

Section: Introductionmentioning

confidence: 99%

Pricing multi-asset derivatives by variational quantum algorithms

Kubo¹,

Miyamoto²,

Mitarai³

et al. 2022

Preprint

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Pricing a multi-asset derivative is an important problem in financial engineering, both theoretically and practically. Although it is suitable to numerically solve partial differential equations to calculate the prices of certain types of derivatives, the computational complexity increases exponentially as the number of underlying assets increases in some classical methods, such as the finite difference method. Therefore, there are efforts to reduce the computational complexity by using quantum computation. However, when solving with naive quantum algorithms, the target derivative price is embedded in the amplitude of one basis of the quantum state, and so an exponential complexity is required to obtain the solution. To avoid the bottleneck, the previous study [Miyamoto and Kubo, IEEE Transactions on Quantum Engineering, 3, 1-25 ( 2022)] utilizes the fact that the present price of a derivative can be obtained by its discounted expected value at any future point in time and shows that the quantum algorithm can reduce the complexity. In this paper, to make the algorithm feasible to run on a small quantum computer, we use variational quantum simulation to solve the Black-Scholes equation and compute the derivative price from the inner product between the solution and a probability distribution. This avoids the measurement bottleneck of the naive approach and would provide quantum speedup even in noisy quantum computers. We also conduct numerical experiments to validate our method. Our method will be an important breakthrough in derivative pricing using small-scale quantum computers.

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“…Indeed, the emergence of scalable quantum technologies will affect forecasting, pricing and data science, and will undoubtedly have an economic impact in the following years [8,9]. Certainly, there already exist several efforts in this direction, for instance, an attempt to predict financial crashes [10,11], the application of the principal component analysis to interest-rate correlation matrices [12], quantum methods for portfolio optimization [13][14][15][16][17], quantum generative models for finance [18], a quantum model for pricing collateral debt obligations [19], a protocol to optimize the exchange of securities and cash between parties [20], an application to improve Monte Carlo methods in risk analysis [21,22], among many others. Regarding the option pricing problem, it has been studied the problem of solving Black-Scholes model employing Monte Carlo methods to solve the associated stochastic differential equation (SDE).…”

Section: Introductionmentioning

confidence: 99%