Neural Network for valuing Bitcoin options under jump-diffusion and market sentiment model

ArXiv ID: 2310.09622 “View on arXiv”

Authors: Unknown

Abstract

Cryptocurrencies and Bitcoin, in particular, are prone to wild swings resulting in frequent jumps in prices, making them historically popular for traders to speculate. A better understanding of these fluctuations can greatly benefit crypto investors by allowing them to make informed decisions. It is claimed in recent literature that Bitcoin price is influenced by sentiment about the Bitcoin system. Transaction, as well as the popularity, have shown positive evidence as potential drivers of Bitcoin price. This study considers a bivariate jump-diffusion model to describe Bitcoin price dynamics and the number of Google searches affecting the price, representing a sentiment indicator. We obtain a closed formula for the Bitcoin price and derive the Black-Scholes equation for Bitcoin options. We first solve the corresponding Bitcoin option partial differential equation for the pricing process by introducing artificial neural networks and incorporating multi-layer perceptron techniques. The prediction performance and the model validation using various high-volatile stocks were assessed.

Keywords: bivariate jump-diffusion, Bitcoin, sentiment analysis, neural networks, option pricing

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper employs dense mathematics, including a bivariate jump-diffusion SDE model, closed-form derivations, PDE solving, and neural network approximation techniques, scoring high on complexity. However, the empirical rigor is low as the excerpt focuses on theoretical derivations and methodology, with only mentions of validation on stocks rather than detailed backtests, datasets, or implementation metrics for Bitcoin.

  flowchart TD
    A["Research Goal: <br>Value Bitcoin Options under Jump-Diffusion & Sentiment"] --> B["Methodology: <br>Bivariate Jump-Diffusion Model"]
    
    B --> C["Inputs: <br>Bitcoin Price & Google Search Volume"]
    
    C --> D["Process: <br>Derive Closed-Form Solution & Black-Scholes PDE"]
    
    D --> E["Process: <br>Artificial Neural Network (MLP) Solver"]
    
    E --> F["Outcomes: <br>Closed Formula, Validated Model & Performance Metrics"]
    
    style A fill:#e1f5fe
    style F fill:#e8f5e8