Online adaptive machine learning based algorithm for implied volatility surface modeling

Yaxiong Zeng*, Diego Klabjan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)376-391
Number of pages16
JournalKnowledge-Based Systems
StatePublished - Jan 1 2019


  • FPGA application
  • Implied volatility surface
  • Kernel methods
  • Machine learning
  • Online adaptive learning
  • Option pricing
  • Stochastic gradient descent
  • Support vector regression

ASJC Scopus subject areas

  • Management Information Systems
  • Software
  • Information Systems and Management
  • Artificial Intelligence


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