• Corpus ID: 250264637

Pricing multi-asset derivatives by variational quantum algorithms

@inproceedings{Kubo2022PricingMD,
  title={Pricing multi-asset derivatives by variational quantum algorithms},
  author={Kenji Kubo and Koichi Miyamoto and Kosuke Mitarai and Keisuke Fujii},
  year={2022}
}
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… 

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References

SHOWING 1-10 OF 56 REFERENCES

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

This paper considers the local volatility (LV) model, in which the volatility of the underlying asset price depends on the price and time, and discusses the state preparation step of the QAE, or equivalently, the implementation of the asset price evolution.

Quantum Algorithms for Portfolio Optimization

This work develops the first quantum algorithm for the constrained portfolio optimization problem and provides some experiments to bound the problem-dependent factors arising in the running time of the quantum algorithm, suggesting that for most instances the quantum algorithms can potentially achieve an O(n) speedup over its classical counterpart.

Quantum computational finance: Monte Carlo pricing of financial derivatives

This work presents a quantum algorithm for the Monte Carlo pricing of financial derivatives and shows how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimate for the price with high confidence.

Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

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.

Toward pricing financial derivatives with an IBM quantum computer

This manuscript is a first step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives, and shows indeed that practical applications of quantum computers in finance will be achievable in the near future.

Variational quantum simulations of stochastic differential equations

A quantum-classical hybrid algorithm that solves SDEs based on variational quantum simulation (VQS) based on trinomial tree structure with discretization and embedding the probability distributions of the SDE variables in the amplitudes of the quantum state.

A variational quantum algorithm for the Feynman-Kac formula

We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic

Quantum speedup of Monte Carlo integration with respect to the number of dimensions and its application to finance

It is pointed out that the number of repeated operations in the high-dimensional integration can be reduced by a combination of the nested QAE and the use of pseudorandom numbers (PRNs), if the integrand has the separable form with respect to contributions from distinct random numbers.

A Survey of Quantum Computing for Finance

A comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning, describing how these solutions, adapted to work on a quantum computer, can potentially help to solve financial problems more efficiently and accurately.

Quantum Computation for Pricing the Collateralized Debt Obligations

This work implements two typical CDO models, the single-factor Gaussian copula model and Normal Inverse GaussianCopula model, and applies quantum amplitude estimation as an alternative to Monte Carlo simulation for CDO pricing, significantly broadening the application scope for quantum computing in finance.
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