Paper: arXiv 2506.22888

Authors: Jirong Zhuang, Xuan Wu

Abstract

Constructing the Implied Volatility Surface (IVS) is a challenging task in quantitative finance due to the complexity of real markets and the sparsity of market data. Structural models like Stochastic Alpha Beta Rho (SABR) model offer interpretability and theoretical consistency but lack flexibility, while purely data-driven methods such as Gaussian Process regression can struggle with sparse data. We introduce SABR-Informed Multi-Task Gaussian Process (SABR-MTGP), treating IVS construction as a multi-task learning problem. Our method uses a dense synthetic dataset from a calibrated SABR model as a source task to inform the construction based on sparse market data (the target task). The MTGP framework captures task correlation and transfers structural information adaptively, improving predictions particularly in data-scarce regions. Experiments using Heston-generated ground truth data under various market conditions show that SABR-MTGP outperforms both standard Gaussian process regression and SABR across different maturities. Furthermore, an application to real SPX market data demonstrates the method’s practical applicability and its ability to produce stable and realistic surfaces. This confirms our method balances structural guidance from SABR with the flexibility needed for market data.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical frameworks including Gaussian Processes, SABR dynamics, and multi-task learning with detailed kernel formulations, which indicates high math complexity. It also demonstrates high empirical rigor through Heston-generated synthetic data tests, real SPX market data applications, and specific performance comparisons against baselines.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Improve Implied Volatility Surface<br>Construction for Sparse Data"] --> B{"Key Methodology:<br>SABR-Informed Multi-Task GP"}
  
  B --> C["Data Preparation:<br>Use Synthetic SABR Data<br>as Source Task"]
  B --> D["Data Preparation:<br>Use Sparse Market Data<br>as Target Task"]
  
  C & D --> E["Computational Process:<br>Transfer Structural Information<br>from SABR to GP via Multi-Task Learning"]
  
  E --> F["Key Findings:<br>Outperforms Standard GP & SABR<br>on Heston & Real SPX Data"]
  E --> G["Outcome:<br>Balance of Structural Guidance<br>and Market Flexibility"]