A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Kastoryano, Michael J.; Pancotti, Nicola

doi:10.48550/arxiv.2203.02804

Cited by 2 publications

(3 citation statements)

References 20 publications

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“…• Pricing of standard ('vanilla'), path-dependent (e.g. barrier and Asian) and multiasset options in a Black-Scholes [9] and local volatility [28] framework [4,18,33,38,51,54,64,72,73,75,76,80] • Pricing of options under a stochastic volatility [16] and jump-diffusion process [95] • Pricing of American-style options [27,62] • Pricing of interest-rate derivatives with a multi-factor model [58,84] • Pricing of collateralised debt obligations (CDOs) [83] Risk measurement. In a financial context, 'risk' usually refers to an adverse event associated with a (financial) loss.…”

Section: Research Landscape In Quantitative Financementioning

confidence: 99%

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Quantum computing for financial risk measurement

Wilkens¹,

Moorhouse

2023

Quantum Inf Process

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Quantum computing allows a significant speed-up over traditional CPU- and GPU-based algorithms when applied to particular mathematical challenges such as optimisation and simulation. Despite promising advances and extensive research in hard- and software developments, currently available quantum systems are still largely limited in their capability. In line with this, practical applications in quantitative finance are still in their infancy. This paper analyses requirements and concrete approaches for the application to risk management in a financial institution. On the examples of Value-at-Risk for market risk and Potential Future Exposure for counterparty credit risk, the main contribution lies in going beyond textbook illustrations and instead exploring must-have model features and their quantum implementations. While conceptual solutions and small-scale circuits are feasible at this stage, the leap needed for real-life applications is still significant. In order to build a usable risk measurement system, the hardware capacity—measured in number of qubits—would need to increase by several magnitudes from their current value of about $$10^2$$ 10 2 . Quantum noise poses an additional challenge, and research into its control and mitigation would need to advance in order to render risk measurement applications deployable in practice. Overall, given the maturity of established classical simulation-based approaches that allow risk computations in reasonable time and with sufficient accuracy, the business case for a move to quantum solutions is not very strong at this point.

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Section: Research Landscape In Quantitative Financementioning

confidence: 99%

“…Practically, this entails flipping each bit with the given probability on every affected operation in the circuit. Continuing the work on a quantum simulator, 51 the model is applied to the example for counterparty credit risk from Sect. 5.…”

Section: Influence Of Quantum Noisementioning

confidence: 99%

Quantum computing for financial risk measurement

Wilkens¹,

Moorhouse

2023

Quantum Inf Process

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“…This humble looking network is a powerful tool for an increasingly diverse portfolio of applications, including modeling fluid flow and other processes described by differential equations [GLD + 22], simulating (and sometimes beating!) quantum computers [SVS + 22], high-performance matrix computations [RO22], and financial modeling [KP22]. If you are interested in using tensor trains or matrix product states, a good way to get started is to use the ITensor software [FWS22] which offers tools for instantiating and performing operations on this kind of data structure.…”

Section: Mps or Tensor Train Networkmentioning

confidence: 99%

From Rotations and Groups to Tensor Networks

Stoudenmire¹

2023

TJTMI

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Even the simplest mathematical concepts can have surprisingly deep struc-ture and hidden connections to other topics. In this article we explore rotations of two-dimensional objects. After viewing rotations first concretely as small matrices, then more abstractly as members of a "group", we consider how rotations transform simple functions (x, y, x − y , etc.) and their products. Transforming products of three or more functions is best captured by introducing multi-dimensional generalizations of vectors and matrices known as tensors and chaining these tensors together. The resulting object known as a tensor train (or matrix product state) is one of the most powerful computational tools for applications such as modeling fluid flows, understanding properties of metals and crystals, predicting financial markets, and simulating quantum computers.

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A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Cited by 2 publications

References 20 publications

Quantum computing for financial risk measurement

Quantum computing for financial risk measurement

From Rotations and Groups to Tensor Networks

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