Quantum Computation for Pricing the Collateralized Debt Obligations

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

doi:10.48550/arxiv.2008.04110

Cited by 5 publications

(7 citation statements)

References 32 publications

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“…Since F is explicitly given as (11), the sum of the Kronecker products of tridiagonal matrices, construction of O F,1 and O F,2 is straightforward. On the other hand, fpay and C are highly problem-dependent, and so are O fpay and O C .…”

Section: Generating the Derivative Price Vectormentioning

confidence: 99%

“…Then, we can evaluate the complexity by substituting s and A in (28) with the sparsity and norm of F, respectively. The sparsity of F is O(d 2 ), since the matrices constituting F as (11) have sparsity at most 4 and the total number of them is O(d 2 ). Besides,…”

Section: A22 Upper Bound the Integral On The Outside Of The Boundariesmentioning

confidence: 99%

“…Since large financial institutions perform enormous computational tasks in their daily business 2 , it is naturally expected that quantum computers will tremendously speedup them and make a large impact on the industry. In fact, some recent papers have already discussed applications of quantum algorithms to concrete problems in financial engineering: for example, derivative pricing [4][5][6][7][8][9][10][11][12][13][14][15][16], risk measurement [17][18][19], portfolio optimization [20][21][22], and so on. See [23][24][25] as comprehensive reviews.…”

Section: Introductionmentioning

confidence: 99%

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Pricing multi-asset derivatives by finite difference method on a quantum computer

Miyamoto¹,

Kubo²

2021

Preprint

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Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this paper, we focus on derivative pricing based on solving the Black-Scholes partial differential equation by finite difference method (FDM), which is a suitable approach for some types of derivatives but suffers from the curse of dimensionality, that is, exponential growth of complexity in the case of multiple underlying assets. We propose a quantum algorithm for FDM-based pricing of multi-asset derivative with exponential speedup with respect to dimensionality compared with classical algorithms. The proposed algorithm utilizes the quantum algorithm for solving differential equations, which is based on quantum linear system algorithms. Addressing the specific issue in derivative pricing, that is, extracting the derivative price for the present underlying asset prices from the output state of the quantum algorithm, we present the whole of the calculation process and estimate its complexity. We believe that the proposed method opens the new possibility of accurate and high-speed derivative pricing by quantum computers.

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Section: Generating the Derivative Price Vectormentioning

confidence: 99%

Section: A22 Upper Bound the Integral On The Outside Of The Boundariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Pricing multi-asset derivatives by finite difference method on a quantum computer

Miyamoto¹,

Kubo²

2021

Preprint

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show abstract

“…Quantum computing promises to achieve an exponential speedup to tackle certain computational tasks compared with the classical computers [11,18,21,32,33,46,47]. Although quantum technologies are continuously improving, current quantum devices are still qualified as Noisy Intermediate-Scale Quantum (NISQ) hardware [41], with several physical constraints.…”

Section: Introductionmentioning

confidence: 99%

Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era

Niu,

Todri-Sanial

2021

Preprint

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As NISQ devices have several physical limitations and unavoidable noisy quantum operations, only small circuits can be executed on a quantum machine to get reliable results. This leads to the quantum hardware under-utilization issue. Here, we address this problem and improve the quantum hardware throughput by proposing a multiprogramming approach to execute multiple quantum circuits on quantum hardware simultaneously. We first introduce a parallelism manager to select an appropriate number of circuits to be executed at the same time. Second, we present two different qubit partitioning algorithms to allocate reliable partitions to multiple circuits -a greedy and a heuristic. Third, we use the Simultaneous Randomized Benchmarking protocol to characterize the crosstalk properties and consider them in the qubit partition process to avoid crosstalk effect during simultaneous executions. Finally, we enhance the mapping transition algorithm to make circuits executable on hardware using a decreased number of inserted gates. We demonstrate the performance of our multi-programming approach by executing circuits of different sizes on IBM quantum hardware simultaneously. We also investigate this method on VQE algorithm to reduce its overhead.

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“…Financial firms have a lot of heavy computational tasks in their daily business 2 , and therefore the speed-up of such tasks by quantum computers are expected to provide a large impact. For example, previous papers studied option pricing [7][8][9][10][11][12][13][14][15][16][17][18], risk measurement [19][20][21][22], portfolio optimization [23][24][25], and so on.…”

Section: Introductionmentioning

confidence: 99%

Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

Miyamoto¹

2021

Preprint

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Pricing of financial derivatives, in particular early exercisable options such as Bermudan options, is an important but heavy numerical task in financial institutions, and its speed-up will provide a large business impact. Recently, applications of quantum computing to financial problems have been started to be investigated. In this paper, we first propose a quantum algorithm for Bermudan option pricing. This method performs the approximation of the continuation value, which is a crucial part of Bermudan option pricing, by Chebyshev interpolation, using the values at interpolation nodes estimated by quantum amplitude estimation. In this method, the number of calls to the oracle to generate underlying asset price paths scales as O(ǫ −1 ), where ǫ is the error tolerance of the option price. This means the quadratic speed-up compared with classical Monte Carlo-based methods such as least-squares Monte Carlo, in which the oracle call number is O(ǫ −2 ).

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Quantum Computation for Pricing the Collateralized Debt Obligations

Cited by 5 publications

References 32 publications

Pricing multi-asset derivatives by finite difference method on a quantum computer

Pricing multi-asset derivatives by finite difference method on a quantum computer

Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era

Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

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