FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs

Paper: arXiv 2303.00859

Authors: Vedant Choudhary, Sebastian Jaimungal, Maxime Bergeron

Abstract

We introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices. We do so using a combination of functional data analysis and neural stochastic differential equations (SDEs) combined with a probability integral transform penalty to reduce model misspecification. We demonstrate that learning the joint dynamics of IV surfaces and prices produces market scenarios that are consistent with historical features and lie within the sub-manifold of surfaces that are essentially free of static arbitrage. Finally, we demonstrate that delta hedging using the simulated surfaces generates profit and loss (P&L) distributions that are consistent with realised P&Ls.

Complexity vs Empirical Score

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

Why this score: The paper presents an advanced, highly novel approach combining Functional Data Analysis (FDA) and Neural SDEs for multi-asset implied volatility surface simulation. Empirical evaluation is strong, validating static arbitrage constraints and realistic delta hedging P&L distributions against historical data.

Research Flowchart

  flowchart TD
    A[Goal: Simulate Realistic Multi-Asset IV Surfaces & Asset Prices] --> B[Data Inputs: Historical Options Surfaces & Underlying Asset Prices]
    B --> C[Dimension Reduction: Functional Principal Component Analysis - FPCA]
    C --> D[Joint Dynamics: Neural SDEs + PIT Penalty for Arbitrage-Free Surfaces]
    D --> E[Outcome: Realistic Market Scenarios Consistent with Static Arbitrage Constraints]
    E --> F[Validation: Delta Hedging P&L Distributions Match Realized P&Ls]