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

摘要

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.