Multiscaling in the Rough Bergomi Model: A Tale of Tails

Battle Count: 72

The findings have moderate relevance to quantitative trading. The paper's conclusion that multiscaling in rough volatility models is primarily distributional rather than temporal has implications for: (1) risk management - practitioners should focus on distributional properties rather than fractal scaling laws; (2) option pricing - the model's value for capturing implied volatility surfaces remains intact; (3) strategy design - multiscaling should not be interpreted as evidence of market inefficiency exploitable through temporal patterns. However, the paper is primarily theoretical/methodological rather than directly applicable to trading strategy development.

The methodology involves multiple components: (1) simulating the rough Bergomi model with fractional Brownian motion (requires Davies-Harte algorithm), (2) computing generalized Hurst exponents via log-log regression with WLS, (3) generating matched fBm surrogates, (4) generating shuffled surrogates via Fisher-Yates permutation, (5) performing permutation-based hypothesis tests with distance statistics, (6) data-driven tail exponent estimation via MLE of α-stable distributions, and (7) optimal scale selection via R² thresholding. Each component is well-defined but the full pipeline requires careful implementation and parameter tuning.

The paper provides detailed mathematical formulations, parameter choices (ξ₀=0.1, ρ=-0.9, η=1.9, H∈[0.001,0.2]), simulation settings (n=1000 simulations, N=10000 observations), and algorithmic descriptions (Davies-Harte method, Fisher-Yates shuffle). However, no code repository is provided, and the specific implementation details for the WLS regression and surrogate generation would need to be reconstructed from the text.