Alice Roberts
Title: A Filtering-Based Approach for Implied Volatility Surface Modelling
Date: August 14th, 2025
Time: 1:00pm
Location: LIB 7200 & Zoom
Supervised by: Jean-Fran莽ois B茅gin
Abstract:
The implied volatility surface is notoriously difficult to model due to its complex shape and the challenge of accurately capturing its dynamics and evolution over time. This report focuses on its modelling. We extend the factor-based specification of Fran莽ois et al. (2022) by embedding their implied volatility surface model within a state-space framework, where the surface coefficients follow a vector autoregressive process. Using the Kalman filter, we recursively update these parameters on a daily basis. Employing Standard & Poor鈥檚 500 option data from January 1996 to December 2019, we recalibrate benchmark models, including the polynomial regression of Gon莽alves and Guidolin (2006), the piecewise parametric specification of Chalamandaris and Tsekrekos (2011), and the stochastic volatility model of Heston (1993), by minimizing squared fitting errors each day. We assess the in-sample performance of our new framework and other benchmarks using the root-mean-square error and the absolute relative percentage error. We also analyze the time-series behaviour of the latent surface factors and visualize cross-sectional accuracy through reconstructed implied volatility surfaces.