Speed-up credit exposure calculations for pricing and risk management

Glau, Kathrin; Pachon, Ricardo; Pötz, Christian

doi:10.1080/14697688.2020.1781236

Cited by 8 publications

(7 citation statements)

References 15 publications

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“…In fact, the idea that we approximate the continuation value by Chebyshev interpolation is not novel. There are some classical methods for Bermudan option pricing based on Chebyshev interpolation [44][45][46][47][48][49][50]. However, in addition to whether we use QAE or other classical methods for calculating the nodal continuation values, there are the following differences between the above proposed method and the existing methods.…”

Section: Comparison With Existing Chebyshev Interpolation-based Methodsmentioning

confidence: 99%

“…As far as the author knows, this is the first proposal on the quantum method for Bermudan option pricing. Chebyshev interpolation is a widely used method for function approximation, 5 and has already been used in some (classical) methods for Bermudan option pricing [44][45][46][47][48][49][50]. In the proposed method, given the access to the quantum circuit (or, the oracle) for time evolution of underlying asset prices, we calculate the continuation values at the interpolation nodes by the quantum algorithm, and find Chebyshev interpolation using these values.…”

Section: Introductionmentioning

confidence: 99%

“…[47][48][49][50] considered the more general case, where the values of ρ and m are different for different directions in R d . In this paper, we take common values of ρ and m for every direction, for simplicity.…”

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confidence: 99%

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Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

Miyamoto

2022

EPJ Quantum Technol.

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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 $\widetilde{O}(\epsilon ^{-1})$ O ˜ ( ϵ − 1 ) , where ϵ 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 $\widetilde{O}(\epsilon ^{-2})$ O ˜ ( ϵ − 2 ) .

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Section: Comparison With Existing Chebyshev Interpolation-based Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

Miyamoto

2022

EPJ Quantum Technol.

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Section: E Comparison With Existing Chebyshev Interpolation-based Met...mentioning

confidence: 99%

“…As far as the author knows, this is the first proposal on the quantum method for Bermudan option pricing. Chebyshev interpolation is a widely used method for function approximation 5 , and has already been used in some (classical) methods for Bermudan option pricing [44][45][46][47][48][49][50]. In the proposed method, given the access to the quantum circuit (or, the oracle) for time evolution of underlying asset prices, we calculate the continuation values at the interpolation nodes by the quantum algorithm, and find Chebyshev interpolation using these values.…”

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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Neural network expression rates and applications of the deep parametric PDE method in counterparty credit risk

Glau

Wunderlich

2023

Ann Oper Res

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The recently introduced deep parametric PDE method combines the efficiency of deep learning for high-dimensional problems with the reliability of classical PDE models. The accuracy of the deep parametric PDE method is determined by the best-approximation property of neural networks. We provide (to the best of our knowledge) the first approximation results, which feature a dimension-independent rate of convergence for deep neural networks with a hyperbolic tangent as the activation function. Numerical results confirm that the deep parametric PDE method performs well in high-dimensional settings by presenting in a risk management problem of high interest for the financial industry.

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Speed-up credit exposure calculations for pricing and risk management

Cited by 8 publications

References 15 publications

Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

Bermudan option pricing by quantum amplitude estimation and Chebyshev interpolation

Neural network expression rates and applications of the deep parametric PDE method in counterparty credit risk

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