Robust option pricing with volatility term structure -- An empirical study for variance options

Paper: arXiv 2312.09201

Authors: Alexander M. G. Cox, Annemarie M. Grass

Abstract

The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the 2008 financial crisis, and can be used to understand the extent to which a model-based price is sensitive to the underlying model assumptions. Common approaches involve pricing exotic derivatives such as variance options by incorporating market data through implied volatility. The existing literature focuses largely on incorporating implied volatility information corresponding to the maturity of the exotic option. In this paper, we aim to explain how intermediate data can and should be incorporated. It is natural to expect that this additional information will improve the robust pricing bounds. To investigate this question, we consider variance options, where the bounds of the informed robust pricing problem are known. We proceed to conduct an empirical study uncovering a surprising finding: Contrary to common belief, the incorporation of more information does not lead to an improvement of the robust pricing bounds.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong combination of theoretical robust option pricing framework and empirical testing on variance options. Its counterintuitive finding—that incorporating intermediate term structure data does not tighten robust bounds—offers high novelty and practical insight for quantitative risk management.

Research Flowchart

  flowchart TD
    A["Research Question: Does incorporating intermediate implied volatility data improve robust pricing bounds for variance options?"] --> B["Inputs: Market Data & Volatility Term Structure"]
    B --> C["Pricing Framework: Informed Robust Option Pricing (No-Arbitrage Bounds)"]
    C --> D["Empirical Study: Compute Upper & Lower Price Bounds"]
    D --> E["Comparison: Single-Maturity vs. Intermediate Multi-Maturity Information"]
    E --> F["Key Finding: Intermediate data does NOT improve robust pricing bounds"]