Paper: arXiv 2412.00658

Abstract

A new modular approximate Bayesian inferential framework is proposed that enables fast calculation of probabilistic predictions of future option prices. We exploit multiple information sources, including daily spot returns, high-frequency spot data and option prices. A benefit of this modular Bayesian approach is that it allows us to work with the theoretical option pricing model, without needing to specify an arbitrary statistical model that links the theoretical prices to their observed counterparts. We show that our approach produces accurate probabilistic predictions of option prices in realistic scenarios and, despite not explicitly modelling pricing errors, the method is shown to be robust to their presence. Predictive accuracy based on the Heston stochastic volatility model, with predictions produced via rapid real-time updates, is illustrated empirically for short-maturity options.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs high-level mathematical concepts including stochastic calculus, Heston stochastic volatility models, and approximate Bayesian computation, requiring advanced statistical and econometric theory. It also demonstrates empirical rigor through simulation exercises, robustness checks, and an application to S&P500 index data with real-world implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Fast Probabilistic Predictions of Future Option Prices"] --> B["Methodology<br>Modular Approximate Bayesian Inference"]
  
  B --> C{"Data Integration"}
  C --> C1["Daily Spot Returns"]
  C --> C2["High-Frequency Spot Data"]
  C --> C3["Option Prices"]
  
  C --> D["Theoretical Model<br>Heston Stochastic Volatility Model"]
  
  D --> E["Computational Process<br>Rapid Real-Time Bayesian Updates"]
  
  E --> F["Key Findings"]
  F --> F1["Accurate Probabilistic Predictions"]
  F --> F2["Robust to Pricing Errors"]
  F --> F3["No Arbitrary Statistical Model Needed"]

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