The Function

The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among other things, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is computationally very involved. We present a novel numerical method to compute the VaR and ES of a given portfolio within the stochastic holding period framework. Two approaches are considered, the delta-gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-ofthe-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump-diffusion model and the Kou model. Central to this procedure is the application of the SWIFT method developed for option pricing, that appears to be a very efficient and robust Fourier inversion method for risk management purposes.

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“…Using the classical Vieta's formula [12], the cardinal sine can be expressed as the following infinite product,…”

Section: Shannon Wavelets and Swift Methodsmentioning

confidence: 99%

Computation of market risk measures with stochastic liquidity horizon

Colldeforns-Papiol

Ortiz-Gracia

2018

Journal of Computational and Applied Mathematics

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“…Using the classical Vieta's formula (Gearhart and Shultz, 1990), the cardinal sinus can be expressed as the following infinite product…”

Section: Swift Methodsmentioning

confidence: 99%

A Dimension Reduction Shannon-Wavelet Based Method for Option Pricing

Dang

Ortiz-Gracia

2017

J Sci Comput

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We present a robust and highly efficient dimension reduction Shannon-wavelet method for computing European option prices and hedging parameters under a general jump-diffusion model with square-root stochastic variance and multi-factor Gaussian interest rates. Within a dimension reduction framework, the option price can be expressed as a two-dimensional integral that involves only (i) the value of the variance at the terminal time, and (ii) the time-integrated variance process conditional on this value. A Shannon wavelet inverse Fourier technique is developed to approximate the conditional density of the time-integrated variance process. Furthermore, thanks to the excellent approximation properties of Shannon wavelets, the overall pricing procedure is reduced to the evaluation of just a single integral that involves only the density of the terminal variance value. This single integral can be accurately evaluated, since the density of the variance at the terminal time is known in closed-form. We develop sharp approximation error bounds for the option price and hedging parameters. Numerical experiments confirm the robustness and impressive efficiency of the method.

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“…In our publications (Quine & Abrarov, 2013;Abrarov & Quine 2015a) we have introduced the following product-to-sum identity k m=1 cos t 2 m = 1 2 k−1 2 k−1 m=1 cos m − 1/2 2 k−1 t , ∀k ≥ 1 and since (Gearhart & Shultz, 1990;Weisstein, 2019c)…”

Section: Appendix Bmentioning

confidence: 99%

Reviewer Acknowledgements for Earth Science Research, Vol. 8, No. 2

Luo¹

2019

ESR

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Earth Science Research wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated. Earth Science Research is recruiting reviewers for the journal. If you are interested in becoming a reviewer, we welcome you to join us. Please find the application form and details at http://www.ccsenet.org/reviewer and e-mail the completed application form to esr@ccsenet.org. Reviewers for Volume 8, Number 2 Bahareh Shoghli, University Of North Dakota, USA Esmat Ahmed Abou El-Anwar, National Research Centre, Egypt Fehmi ARIKAN, General Directorate of Mineral Research and Exploration Company, Turkey Helber Gomes, Federal University of São Paulo and Center for Weather Forecasting and Climate Research, Brazil Iyad Ahmed Abboud, Taibah University, Jordan Khalid Ubeid, Al-Azhar University-Gaza, Palestine P. Sathees Kumar, Mohamed Sathak Engineering College, INDIA Sanjeet Kumar Verma, University of Campinas, Brazil Saumitra Misra, University of KwaZulu-Natal, South Africa

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The Function

Cited by 10 publications

References 5 publications

Computation of market risk measures with stochastic liquidity horizon

Computation of market risk measures with stochastic liquidity horizon

A Dimension Reduction Shannon-Wavelet Based Method for Option Pricing

Reviewer Acknowledgements for Earth Science Research, Vol. 8, No. 2

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