Modeling Stock Returns and Volatility Using Bivariate Gamma Generalized Laplace Law

Battle Count: 95

The paper provides a tractable parametric model for joint modeling of stock returns and volatility with heavy tails and skewness, which is directly relevant to risk management, option pricing, and volatility forecasting in quantitative trading. The MLE reduces to simple weighted least squares, making it computationally efficient. However, it is primarily a statistical/distributional paper rather than a trading strategy paper, and the IID assumption (after transformation) limits direct application to high-frequency trading. The stochastic volatility interpretation and connection to VIX data make it practically useful for volatility-based strategies.

The MLE for delta, mu, and sigma^2 has explicit closed-form solutions equivalent to weighted least squares regression (very simple). The MLE for beta is also closed-form given alpha. However, the MLE for alpha requires solving a transcendental equation numerically (log(alpha) - psi(alpha) = log(X_bar) - log(X_bar_geometric)). The asymptotic theory for alpha <= 1 involves stable subordinators, which are complex to implement for inference. Overall, point estimation is straightforward; full statistical inference requires more sophistication.

The paper provides explicit closed-form expressions for all MLEs, detailed simulation parameters (sample sizes n=50,500; shape parameters alpha=0.25,1,2,5; beta=1; 5000 repetitions), and uses publicly available data from Yahoo Finance (weekly data Sept 2019 - Sept 2024). The numerical solution for alpha requires standard methods. However, no code repository is provided.