Automatic differentiation for diffusion operator integral variance reduction

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Automatic differentiation for diffusion operator integral variance reduction. / Auster, Johan Christoffer K.

In: Journal of Computational Finance, Vol. 25, No. 4, 2, 18.02.2022, p. 27-53.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Auster, JCK 2022, 'Automatic differentiation for diffusion operator integral variance reduction', Journal of Computational Finance, vol. 25, no. 4, 2, pp. 27-53. https://doi.org/10.21314/JCF.2021.013

APA

Auster, J. C. K. (2022). Automatic differentiation for diffusion operator integral variance reduction. Journal of Computational Finance, 25(4), 27-53. [2]. https://doi.org/10.21314/JCF.2021.013

Vancouver

Auster JCK. Automatic differentiation for diffusion operator integral variance reduction. Journal of Computational Finance. 2022 Feb 18;25(4):27-53. 2. https://doi.org/10.21314/JCF.2021.013

Author

Auster, Johan Christoffer K. / Automatic differentiation for diffusion operator integral variance reduction. In: Journal of Computational Finance. 2022 ; Vol. 25, No. 4. pp. 27-53.

Bibtex

@article{ef903ed7415f4ef9928f598b58f9bd1e,
title = "Automatic differentiation for diffusion operator integral variance reduction",
abstract = "This paper demonstrates applications of automatic differentiation with nested dual numbers in the diffusion operator integral variance-reduction framework originally proposed by Heath and Platen. Combining this estimator with automatic differentiation techniques for computing value function sensitivities allows for a flexible implementation without trade-offs in numerical stability or accuracy. This fully mitigates a key practical shortcoming of the original estimator, as we remove the dependency on error-prone and problem-specific manual calculations. We perform a relative error analysis of the estimator and standard Monte Carlo estimation against the numerical integration solution of the European call option in the Heston model and find computational time savings in excess of three orders of magnitude for the same expected relative errors for an at-the-money option. The implementation is further extended to the valuation of discrete down-and-out barrier call options and floating-strike lookback put options, demonstrating the relative ease of applying the automatic differentiation approach to path-dependent options with monitoring bias corrections.",
keywords = "Faculty of Science, Monte Carlo, automatic differentiation, variance reduction, Heston model, barrier options, lookback options",
author = "Auster, {Johan Christoffer K}",
year = "2022",
month = feb,
day = "18",
doi = "10.21314/JCF.2021.013",
language = "English",
volume = "25",
pages = "27--53",
journal = "Journal of Computational Finance",
issn = "1460-1559",
publisher = "Incisive Media Ltd.",
number = "4",

}

RIS

TY - JOUR

T1 - Automatic differentiation for diffusion operator integral variance reduction

AU - Auster, Johan Christoffer K

PY - 2022/2/18

Y1 - 2022/2/18

N2 - This paper demonstrates applications of automatic differentiation with nested dual numbers in the diffusion operator integral variance-reduction framework originally proposed by Heath and Platen. Combining this estimator with automatic differentiation techniques for computing value function sensitivities allows for a flexible implementation without trade-offs in numerical stability or accuracy. This fully mitigates a key practical shortcoming of the original estimator, as we remove the dependency on error-prone and problem-specific manual calculations. We perform a relative error analysis of the estimator and standard Monte Carlo estimation against the numerical integration solution of the European call option in the Heston model and find computational time savings in excess of three orders of magnitude for the same expected relative errors for an at-the-money option. The implementation is further extended to the valuation of discrete down-and-out barrier call options and floating-strike lookback put options, demonstrating the relative ease of applying the automatic differentiation approach to path-dependent options with monitoring bias corrections.

AB - This paper demonstrates applications of automatic differentiation with nested dual numbers in the diffusion operator integral variance-reduction framework originally proposed by Heath and Platen. Combining this estimator with automatic differentiation techniques for computing value function sensitivities allows for a flexible implementation without trade-offs in numerical stability or accuracy. This fully mitigates a key practical shortcoming of the original estimator, as we remove the dependency on error-prone and problem-specific manual calculations. We perform a relative error analysis of the estimator and standard Monte Carlo estimation against the numerical integration solution of the European call option in the Heston model and find computational time savings in excess of three orders of magnitude for the same expected relative errors for an at-the-money option. The implementation is further extended to the valuation of discrete down-and-out barrier call options and floating-strike lookback put options, demonstrating the relative ease of applying the automatic differentiation approach to path-dependent options with monitoring bias corrections.

KW - Faculty of Science

KW - Monte Carlo

KW - automatic differentiation

KW - variance reduction

KW - Heston model

KW - barrier options

KW - lookback options

U2 - 10.21314/JCF.2021.013

DO - 10.21314/JCF.2021.013

M3 - Journal article

VL - 25

SP - 27

EP - 53

JO - Journal of Computational Finance

JF - Journal of Computational Finance

SN - 1460-1559

IS - 4

M1 - 2

ER -

ID: 300455108