Title: Online Adaptive Machine Learning Based Algorithm for Implied Volatility Surface Modeling,
Abstract: In this work, we design a machine learning based method, online adaptive
primal support vector regression (SVR), to model the implied volatility surface
(IVS). The algorithm proposed is the first derivation and implementation of an
online primal kernel SVR. It features enhancements that allow efficient online
adaptive learning by embedding the idea of local fitness and budget maintenance
to dynamically update support vectors upon pattern drifts. For algorithm
acceleration, we implement its most computationally intensive parts in a Field
Programmable Gate Arrays hardware, where a 132x speedup over CPU is achieved
during online prediction. Using intraday tick data from the E-mini S&P 500
options market, we show that the Gaussian kernel outperforms the linear kernel
in regulating the size of support vectors, and that our empirical IVS algorithm
beats two competing online methods with regards to model complexity and
regression errors (the mean absolute percentage error of our algorithm is up to
13%). Best results are obtained at the center of the IVS grid due to its larger
number of adjacent support vectors than the edges of the grid. Sensitivity
analysis is also presented to demonstrate how hyper parameters affect the error
rates and model complexity.