An Efficient Calibration Framework for Volatility Derivatives under Rough Volatility with Jumps

Battle Count: 85

Highly relevant for quantitative trading desks dealing with VIX options and volatility derivatives. The framework enables real-time or near-real-time calibration (under 20 minutes vs. 24+ hours), which is critical for market-making, hedging, and pricing in volatility products. The rough volatility + jump model captures realistic VIX dynamics. However, the single-day calibration snapshot and data quality issues (arbitrage violations, low liquidity) limit immediate production deployment. The GPU-accelerated pricing engine is directly applicable to trading systems requiring fast option valuation.

High complexity due to multiple interacting components: (1) GPU-accelerated numerical integration via CuPy with arbitrary-precision mpmath validation, (2) complex Volterra-type stochastic integral kernels with piecewise definitions, (3) Fourier-based pricing with incomplete Gamma functions and complex integrals, (4) neural network training pipeline with standardization and regularization, (5) two-stage optimization (GA + L-BFGS-B), (6) data preprocessing with arbitrage filtering, (7) activity index estimation via power variations. Requires expertise in stochastic calculus, numerical methods, deep learning, and optimization. GPU hardware is needed for the CuPy acceleration. The code is available but requires significant domain knowledge to adapt.

Full code repository is publicly available on GitHub (https://github.com/TenghanZhong/GPU-NN-Option-Calibration). Uses open-source tools (PyTorch, CuPy, mpmath, PyGAD, Latin Hypercube Sampling). However, the VIX option data is sourced from Bloomberg terminal, which is proprietary and not freely accessible. Parameter ranges, network architecture, and optimization settings are fully documented. The activity index estimation methodology is clearly described with reproducible formulas.