Paper: arXiv 2405.12988

Abstract

In this paper, our focus lies on the Merton’s jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of methodologies. We adopt an approach that involves implementing different drift, volatility, and jump terms within the model through various machine learning techniques, traditional methods, and statistical methods on price-volume data. Additionally, we introduce a path-dependent Monte Carlo simulation to model cryptocurrency prices, taking into account the volatility and unexpected jumps in prices.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic calculus (Merton jump diffusion SDEs, compound Poisson processes) and path-dependent Monte Carlo simulations, indicating high mathematical density. It is grounded in real cryptocurrency data (BTC/ETH on Binance) and uses statistical metrics (MAE, RMSE, F1-score) for backtesting, but lacks explicit code or complete implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Predict Cryptocurrency Prices"] --> B{"Data Source"}
  B --> C["Historical Price-Volume Data"]
  
  C --> D["Modeling Approach:<br>Merton's Jump Diffusion Model"]
  
  D --> E["Parameter Estimation<br>via ML, Statistical & Traditional Methods"]
  
  E --> F["Path-Dependent<br>Monte Carlo Simulation"]
  
  F --> G["Key Findings"]
  
  G --> H["Improved Price<br>Forecasting Accuracy"]
  G --> I["Effective Modeling of<br>Volatility & Jumps"]

Cited References (32)

  1. Greedy function approximation: A gradient boosting machine. (2001) — link
  2. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options (1993) — link
  3. The Pricing of Options and Corporate Liabilities (1973) — link
  4. Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics (2007) — link
  5. Option pricing when underlying stock returns are discontinuous (1976) — link
  6. XGBoost (2016) — link
  7. Predicting the Price of Bitcoin Using Machine Learning (2018) — link
  8. Volatility estimation for Bitcoin: A comparison of GARCH models (2017) — link
and 24 more
  1. Bitcoin: Medium of exchange or speculative assets? (2017) — link
  2. Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold (2018) — link
  3. A novel cryptocurrency price trend forecasting model based on LightGBM (2018) — link
  4. Lead-Lag relationship between Bitcoin and Ethereum: Evidence from hourly and daily data (2019) — link
  5. Bitcoin price prediction using machine learning: An approach to sample dimension engineering (2019) — link
  6. Deep Learning Approach to Determine the Impact of Socio Economic Factors on Bitcoin Price Prediction (2019) — link
  7. Bitcoin price prediction using Deep Learning Algorithm (2019) — link
  8. A Jump-Diffusion Model for Option Pricing (2002) — link
  9. Bitcoin Price Forecasting via Ensemble-based LSTM Deep Learning Networks (2021) — link
  10. Long and short-term impacts of regulation in the cryptocurrency market (2021) — link
  11. GJR-GARCH Volatility Modeling under NIG and ANN for Predicting Top Cryptocurrencies (2021) — link
  12. Bitcoin price prediction using ARIMA model (2020) — link
  13. Brownian Motion and Stochastic Calculus (1998) — link
  14. Analysis of Bitcoin Price Prediction Using Machine Learning (2023) — link
  15. LSTM–GARCH Hybrid Model for the Prediction of Volatility in Cryptocurrency Portfolios (2023) — link
  16. Metaverse: Cryptocurrency Price Analysis Using Monte Carlo Simulation (2023) — link
  17. Attention-based CNN–LSTM for high-frequency multiple cryptocurrency trend prediction (2023) — link
  18. Forecasting Bitcoin prices using artificial intelligence: Combination of ML, SARIMA, and Facebook Prophet models (2023) — link
  19. Forecasting cryptocurrencies volatility using statistical and machine learning methods: A comparative study (2023) — link
  20. Predicting the cryptocurrency market using social media metrics and search trends during COVID-19 (2024) — link
  21. Comparative Analysis of Machine Learning Algorithms for Daily Cryptocurrency Price Prediction (2024) — link
  22. Profitability trend prediction in crypto financial markets using Fibonacci technical indicator and hybrid CNN model (2024) — link
  23. Probabilistic deep learning and transfer learning for robust cryptocurrency price prediction (2024) — link
  24. A Predictive Model for Digital Currencies Prices using Geometric Brownian Motion Stochastic Differential Equation: A Case Study of the Bitcoin (2024) — link

0 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.