The Limits of Lognormal: Assessing Cryptocurrency Volatility and VaR using Geometric Brownian Motion

Battle Count: 145

The paper is highly relevant to quantitative trading in the cryptocurrency space as it establishes a critical benchmark for risk modeling. The findings directly impact portfolio construction, position sizing, and capital allocation decisions for crypto trading desks. The demonstration that GBM-derived VaR severely underestimates crypto risk (80.67% loss probability vs. 35.27% for equities) has direct implications for risk management in algorithmic trading systems. However, the paper does not propose a trading strategy or signal generation mechanism; it is purely a risk modeling critique. The subsequent papers in the series (jump-diffusion, GARCH improvements) would be more directly actionable for quantitative trading.

The methodology uses well-established, standard techniques: GBM parameter estimation via MLE, portfolio optimization via SLSQP, Cholesky decomposition for correlated random number generation, and Monte Carlo simulation. These are all standard operations available in Python (numpy, scipy, pandas) or R. The implementation is straightforward for anyone with quantitative finance background. However, the paper does not provide code, and careful attention to annualization conventions, trading day counts (252), and covariance matrix estimation is needed for correct implementation.

The methodology is well-described with specific parameters (10,000 simulations, 252 trading days, 5% VaR confidence, one-year horizon, specific tickers). However, no code repository is provided, exact data sources and time periods are not fully specified, and the paper lacks detailed algorithmic pseudocode. The use of standard techniques (GBM, MLE, Cholesky decomposition, SLSQP) aids reproducibility, but the absence of a GitHub link and precise data retrieval instructions limits full replication.