The Delta of a Variance Swap

Battle Count: 193

Highly relevant for quantitative trading desks dealing with variance swaps, VIX products, and option hedging. The paper provides actionable insights: (1) standard SVI/log-moneyness smiles produce zero variance swap delta, which is empirically wrong; (2) the power smile correction with estimated λ values enables proper hedging; (3) the finding that power delta is lower than Black-Scholes delta aligns with practitioner observations about optimal hedge ratios. Directly applicable to derivatives risk management and delta hedging strategies.

Moderate complexity. The analytical results require understanding of integral calculus, Leibniz rule, and homogeneity properties. The SVI calibration involves constrained nonlinear optimization. The power smile implementation is straightforward (multiplicative adjustment). The λ estimation via linear regression is simple. Numerical integration of the Carr-Madan formula requires care with boundaries and convergence. Overall, a competent quantitative analyst could implement the core results in 1-2 weeks.

The paper provides explicit SVI calibration parameters (Tables 1 and 6), detailed formulas, and methodology for numerical integration. However, no code repository or raw data files are explicitly provided. The SVI calibration procedure (constrained least-squares with 60 random restarts) is described but not fully reproducible without the exact SPX option chain data from August 20, 2025. The regression methodology for λ estimation is clearly described.