Fast generation of implied volatility surface: Optimize the traditional numerical analysis and machine learning

Jerome Yen (), Bangren Chen (), KangZhang Wu () and Joseph Yen
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Jerome Yen: Computer and Information Science, University of Macau, P. R. China
Bangren Chen: Computer Science, University of Hong Kong, P. R. China
KangZhang Wu: Electrical and Electronic Engineering, University of Hong Kong, P. R. China
Joseph Yen: Electrical/Mechanical Engineering, University of Macau, P. R. China

International Journal of Financial Engineering (IJFE), 2021, vol. 08, issue 02, 1-24

Abstract: Machine learning has been used in financial markets in supporting many tasks, such as, asset movement forecasting and trading signal generation. Monte Carlo simulation and traditional numerical methods like Newton–Raphson have also been widely applied in financial markets, such as calculation for implied volatility (IV) and pricing of financial products. Is it possible to combine such approaches to more efficiently calculate the IVs to support the generation of IV surface, term structure, and smile? In this paper, we propose a framework that combines the traditional approaches and modern machine learning to support such calculation. In addition, we also propose an adaptive Newton–Raphson to reduce the number of iterations and the possibility of falling into local minimal over the traditional Newton–Raphson. Combining the superiorities of modern machine learning and adaptive Newton–Raphson, an improvement on computation efficiency over pure traditional numerical approaches was achieved. In addition, we also take into consideration of migrating such computation to hardware accelerators such as Graphics cards (GPU) and Field Programmable Gate Arrays (FPGA), to further speed up the computation. Therefore, polynomial regression has also been tested to generate the initial guess of IVs to pave the road of such migration.

Keywords: Implied volatility; machine learning; Newton–Raphson; polynomial regression (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S2424786321500377

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