Fixed-point iterative algorithm for SVI model

Paper: arXiv 2301.07830

Authors: Shuzhen Yang, Wenqing Zhang

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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel fixed-point iterative algorithm combined with least-squares optimization for calibrating the SVI model, supported by theoretical convergence proofs. It provides practical improvements over existing quasi-explicit methods, demonstrating performance on both simulated and real market data, though exact code and dataset details are limited.

Research Flowchart

  flowchart TD
    A[Goal: Develop SVI Calibration Algorithm<br/>Independent of Starting Points] --> B[Inputs: Simulation Data &<br/>Market Option Prices]
    B --> C[Methodology: Hybrid Fixed-Point Iteration<br/>& Least-Squares Optimizer]
    C --> D[Convergence Analysis &<br/>Iterative Computation]
    D --> E[Benchmarking against<br/>Quasi-Explicit SVI Method]
    E --> F[Outcomes: Efficient Calibration,<br/>Guaranteed Convergence & Higher Accuracy]