Paper: arXiv 2503.14829

Authors: Yuhao Liu, Pingping Jiang, Gongqiu Zhang

Abstract

We propose a new financial model, the stochastic volatility model with sticky drawdown and drawup processes (SVSDU model), which enables us to capture the features of winning and losing streaks that are common across financial markets but can not be captured simultaneously by the existing financial models. Moreover, the SVSDU model retains the advantages of the stochastic volatility models. Since there are not closed-form option pricing formulas under the SVSDU model and the existing simulation methods for the sticky diffusion processes are really time-consuming, we develop a deep neural network to solve the corresponding high-dimensional parametric partial differential equation (PDE), where the solution to the PDE is the pricing function of a European option according to the Feynman-Kac Theorem, and validate the accuracy and efficiency of our deep learning approach. We also propose a novel calibration framework for our model, and demonstrate the calibration performances of our models on both simulated data and historical data. The calibration results on SPX option data show that the SVSDU model is a good representation of the asset value dynamic, and both winning and losing streaks are accounted for in option values. Our model opens new horizons for modeling and predicting the dynamics of asset prices in financial markets.

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 introduces a highly novel SVSDU model that successfully incorporates winning and losing streaks into stochastic volatility via two-dimensional sticky diffusion processes. It features rigorous mathematical proofs, a sophisticated deep learning framework (solving high-dimensional parametric PDEs via Feynman-Kac), and extensive empirical validation using SPX options data.

Research Flowchart

  flowchart TD
    A[Research Goal: Model winning & losing streaks via SVSDU Model] --> B[Formulate Pricing PDE via Feynman-Kac Theorem]
    C[Data Inputs: SPX Options & Simulated Market Data] --> D[Train Deep Neural Network to solve High-Dim PDE]
    B --> D
    D --> E[Novel Model Calibration Framework]
    E --> F[Findings: Accurately prices options & captures asset price streaks efficiently]

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