Paper: arXiv 2610.01187

Authors: Long Teng

Abstract

In this work, we study the pricing of American options under stochastic local volatility (SLV) models extended by including stochastic correlation driven by an additional stochastic process. We generalize the class of SLV models by incorporating a flexible stochastic correlation structure. To price options within these extended models, we derive the corresponding reflected forward-backward stochastic differential equations (RBSDEs) and employ data-driven numerical methods to solve them for both pricing and hedging purposes. The RBSDE framework enables the modelling of the future evolution of the option price. Furthermore, we conduct a convergence analysis of the proposed numerical method and present numerical experiments that illustrate the performance of the extended models, as well as the accuracy and efficiency of the RBSDE-based approach.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical approach to a complex problem in quantitative finance, extending existing models with novel stochastic correlation structures. The methodology is rigorously applied and includes convergence analysis and numerical experiments, indicating a strong empirical foundation. The combination of advanced mathematical derivations and practical application for pricing and hedging American options positions it as a significant contribution.

Research Flowchart

  flowchart TD
    A[Research Goal: Price American Options under SLV with Stochastic Correlation] --> B{Key Methodology: RBSDE Framework};
    B --> C[Inputs: Stochastic Local Volatility Models + Stochastic Correlation Process];
    C --> D{Computational Process: Data-driven Numerical Methods};
    D --> E[Outcomes: Option Prices & Hedging Strategies];
    E --> F[Further Outcomes: Convergence Analysis & Numerical Experiments];

Cited References (41)

  1. A deep primal-dual BSDE method for optimal stopping problems — → 2409.06937
  2. Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options — → 2405.02570
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  4. Deep Signature Algorithm for Multidimensional Path-Dependent Options (2022) — link
  5. Randomized Optimal Stopping Problem in Continuous Time and Reinforcement Learning Algorithm (2022) — link
  6. Neural optimal stopping boundary (2022) — link
  7. Deep stochastic optimization in finance (2022) — link
  8. Solving High-Dimensional Optimal Stopping Problems Using Optimization Based Model Order Reduction (2022) — link
and 33 more
  1. Gradient boosting-based numerical methods for high-dimensional backward stochastic differential equations (2021) — link
  2. Option-Implied Correlations and the Price of Correlation Risk (2020) — link
  3. Solving high-dimensional optimal stopping problems using deep learning (2019) — link
  4. Deep backward schemes for high-dimensional nonlinear PDEs (2019) — link
  5. A Review of Tree-based Approaches to solve Forward-Backward Stochastic Differential Equations (2018) — link
  6. QUANTO PRICING IN STOCHASTIC CORRELATION MODELS (2018) — link
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2 of 41 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.