Heston vol-of-vol and the VVIX

Battle Count: 75

Highly relevant for derivatives desks and quantitative risk management. The Heston model is widely used for pricing exotic derivatives (Cliquet options, etc.), and calibration stability is a critical practical concern. The VVIX-based calibration approach directly addresses a major pain point in production systems. However, it is more relevant to derivatives pricing and risk management than to algorithmic trading strategies per se.

The PDE approach requires implementing a 2D finite difference scheme (RKG) with proper boundary conditions and a double replication structure (SPX options -> VIX -> VIX options -> VVIX). The CIR transition density integration is moderately complex. The simple approximation is straightforward but less accurate. Calibration with VVIX constraint requires careful handling of non-monotonicity. Overall, production implementation requires significant numerical expertise.

The paper provides detailed mathematical formulations, parameter sets, and numerical results. However, no code repository is explicitly provided. The Julia QuadGK library is referenced for numerical integration. Market data (SPX500 options as of Oct 8, 2024 and March 15, 2021) would need to be sourced separately. The PDE discretization scheme (RKG) is referenced from prior work by Le Floc'h.