Short-term Volatility Estimation for High Frequency Trades using Gaussian processes (GPs)

ArXiv ID: 2311.10935 “View on arXiv”

Authors: Unknown

Abstract

The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change unexpectedly [“1”]. Price volatility is often detrimental to the return economics, and thus, investors should factor it in whenever making investment decisions, choices, and temporal or permanent moves. It is, therefore, crucial to make necessary and regular short and long-term stock price volatility forecasts for the safety and economics of investors returns. These forecasts should be accurate and not misleading. Different models and methods, such as ARCH GARCH models, have been intuitively implemented to make such forecasts. However, such traditional means fail to capture the short-term volatility forecasts effectively. This paper, therefore, investigates and implements a combination of numeric and probabilistic models for short-term volatility and return forecasting for high-frequency trades. The essence is that one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it is not easy to set price limits in a market due to its free nature and randomness, a Censored GP was used to model the relationship between the corrected stock prices and returns. Forecasting errors were evaluated using the implied and estimated data.

Keywords: Volatility Forecasting, Gaussian Processes, High-Frequency Trading, Time Series Analysis, ARCH/GARCH Models, Equities

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts including Gaussian Processes, censored GP models, and probabilistic regression, but it lacks specific implementation details, backtest metrics, or public code, placing it in a high-math, moderate-rigor zone.

  flowchart TD
    A["Research Goal:<br>Short-term Volatility Estimation for<br>High Frequency Trades using GPs"] --> B{"Data Inputs"}
    B --> B1["High-Frequency Stock Price Data"]
    B --> B2["Numerical Market Prediction<br>NMP Model Outputs"]
    
    B1 & B2 --> C["Methodology: Gaussian Process<br>Framework"]
    C --> C1["Step 1: Price Correction<br>Applied GP to raw NMP outputs"]
    C1 --> C2["Step 2: Censored GP Modeling<br>Relationship between corrected prices<br>and returns"]
    
    C2 --> D["Computational Process"]
    D --> D1["One-day-ahead volatility<br>forecasts generated"]
    D1 --> D2["Error Evaluation<br>Implied vs. Estimated Data"]
    
    D2 --> E{"Key Findings & Outcomes"}
    E --> E1["GP effectively captures<br>short-term volatility"]
    E --> E2["Outperforms traditional<br>ARCH/GARCH models"]
    E --> E3["Improved accuracy for<br>high-frequency trading decisions"]