The Variance Gamma Process for Option Pricing

Battle Count: 70

Highly relevant to quantitative trading, particularly in options market-making, derivative pricing, and risk management. The VG model directly addresses the well-known Black-Scholes biases (volatility smile, excess kurtosis in returns) that affect options trading strategies. The empirical results showing Black-Scholes rejection in 92.3% of weeks for S&P500 options data demonstrate practical significance. The more efficient volatility estimation via mean absolute deviation is directly applicable to trading signal generation. However, the non-uniqueness of the EMM introduces model risk that practitioners must manage.

Moderate to high complexity. The mathematical framework involves Lévy processes, Esscher transforms, and time-subordination theory. Numerical implementation requires: (1) computing the VG density via numerical integration of the Radon-Nikodym derivative, (2) solving the implicit equation for the Esscher parameter h*, (3) numerical integration for option pricing under the risk-neutral VG measure, (4) maximum likelihood estimation with optimization over multiple parameters. The lack of closed-form solutions for the VG CDF and the need for quadrature methods add computational burden. However, the paper provides clear parameterization and the nested structure (VG reduces to BS when ν→0) aids implementation.

The paper provides detailed mathematical derivations, proofs in the appendix, and parameter estimation procedures. However, no code or computational scripts are mentioned. The data sources (Wharton Research Data Services, Federal Reserve Economic Data) are identified but access requires institutional subscriptions. The numerical integration for VG option pricing and Esscher transform calculations would need to be implemented independently.