Fixed-point iterative algorithm for SVI model

TL;DR

This paper introduces a fixed-point iterative algorithm for the SVI model that improves optimization efficiency and convergence, outperforming existing quasi-explicit methods through simulations and market data analysis.

Contribution

The paper develops a novel fixed-point iterative algorithm for the SVI model with proven convergence properties, offering advantages over traditional quasi-explicit methods.

Findings

The algorithm converges efficiently under certain conditions.

Simulation results show improved optimization performance.

Market data validation confirms practical benefits.

Abstract

The stochastic volatility inspired (SVI) model is widely used to fit the implied variance smile. Presently, most optimizer algorithms for the SVI model have a strong dependence on the input starting point. In this study, we develop an efficient iterative algorithm for the SVI model based on a fixed-point and least-square optimizer. Furthermore, we present the convergence results in certain situations for this novel iterative algorithm. Compared with the quasi-explicit SVI method, we demonstrate the advantages of the fixed-point iterative algorithm using simulation and market data.