Solving The Dynamic Volatility Fitting Problem: A Deep Reinforcement Learning Approach
ArXiv ID: 2410.11789 “View on arXiv”
Authors: Unknown
Abstract
The volatility fitting is one of the core problems in the equity derivatives business. Through a set of deterministic rules, the degrees of freedom in the implied volatility surface encoding (parametrization, density, diffusion) are defined. Whilst very effective, this approach widespread in the industry is not natively tailored to learn from shifts in market regimes and discover unsuspected optimal behaviors. In this paper, we change the classical paradigm and apply the latest advances in Deep Reinforcement Learning(DRL) to solve the fitting problem. In particular, we show that variants of Deep Deterministic Policy Gradient (DDPG) and Soft Actor Critic (SAC) can achieve at least as good as standard fitting algorithms. Furthermore, we explain why the reinforcement learning framework is appropriate to handle complex objective functions and is natively adapted for online learning.
Keywords: Deep Reinforcement Learning (DRL), Volatility Fitting, Implied Volatility Surface, Equity Derivatives
Complexity vs Empirical Score
- Math Complexity: 7.5/10
- Empirical Rigor: 4.0/10
- Quadrant: Lab Rats
- Why: The paper utilizes advanced mathematical concepts from reinforcement learning theory and stochastic control, including Markov Decision Processes, value functions, and actor-critic architectures. However, it lacks concrete backtesting results, statistical metrics, or implementation details, relying instead on theoretical assertions and high-level methodology descriptions.
flowchart TD
A["Research Goal<br>Apply DRL to<br>Volatility Fitting"] --> B["Methodology<br>DDPG & SAC Models"]
B --> C["Input Data<br>Market Data &<br>Implied Volatility Surface"]
C --> D["Computational Process<br>Agent-environment Loop<br>with Custom Reward Function"]
D --> E["Key Findings<br>1. Matches Standard Algorithm Performance<br>2. Handles Complex Objectives<br>3. Enables Online Learning"]