Ultra-short-term volatility surfaces

Battle Count: 53

Highly relevant to quantitative trading. The paper addresses the fastest-growing segment of the options market (0DTE to 7-day options, ~70% of SPX volume by 2023). Edgeworth++ provides 28-67x faster pricing than benchmarks for 0DTEs and ~12x faster for full surfaces, making it suitable for real-time market making and high-frequency trading. The model captures the oscillating ATM implied-volatility term structures that classical models cannot, which is critical for accurate hedging and pricing in ultra-short-term derivatives trading. The spot volatility estimation capability is directly useful for risk management. The parsimonious parameterization (7+n parameters) makes daily recalibration feasible.

Moderate to high complexity. The core model requires implementing: (1) the characteristic function expansion up to second order in sqrt(tau) with displacement (Corollary 2), involving matrix operations with DeltaT and Phi-tilde matrices; (2) the piecewise constant displacement structure with recursive calibration; (3) Fourier inversion pricing via the SINC method; (4) daily RMSE minimization over 7+n parameters. The nonparametric nature means parameters are process realizations estimated daily rather than fixed constants. Benchmark comparisons require implementing fractional Riccati ODEs (Rough Heston++) and standard Riccati ODEs (2F Heston Merton). The mathematical derivations are complex but the final pricing formulae are essentially closed-form, reducing computational implementation difficulty relative to simulation-based approaches.

The paper provides detailed mathematical derivations including Theorem 1, Corollary 1, Corollary 2, and Theorem 2 with full proofs in Appendix A. The estimation procedure (RMSE minimization) is clearly specified. Data source (CBOE Datashop) is identified. However, no code or GitHub repository is provided. The SINC Fourier pricing method (Baschetti et al., 2022) with Nf=10^4 nodes is specified. Parameter vectors and model dynamics are fully described. Reproducibility would require implementing the characteristic function expansion, the piecewise displacement structure, and the Fourier inversion pricing algorithm.