Option Pricing with Time-Changed Fractional Brownian Motion: A Fractional Variance Gamma Model

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Highly relevant for quantitative finance practitioners working on option pricing, volatility modeling, and risk management. The fVG model provides a theoretically sound framework for incorporating fractional dynamics (roughness, long-range dependence) into arbitrage-free pricing. The estimated Hurst exponent of ~0.45 for S&P 500 has implications for trading strategies that exploit mean-reversion. However, the lack of closed-form solutions and comprehensive empirical validation limits immediate practical implementation.

High complexity due to: (1) simulation of fBm paths using Wood-Chan method on fine grids, (2) gamma process simulation and time-change evaluation, (3) marked point process representation and compensator computation, (4) multi-start GMM optimization over 5 parameters with 4p moment conditions, (5) conditional distribution approximation via path filtering, (6) Girsanov change of measure for risk-neutral pricing. Requires advanced knowledge of stochastic calculus, semimartingale theory, and numerical methods.

The paper provides detailed mathematical derivations, simulation procedures (Wood-Chan method for fBm, gamma increments), and GMM estimation steps. However, no code or GitHub repository is provided. Data is from CRSP (commercially available). The conditional distribution simulation methodology is described but not fully implemented for option pricing. Proofs are provided in Appendix A.