50k IV Surfaces & 3 Pipelines: Building Rough Bergomi Calibration (Ep.5)

How the experiment is built: 50,000 synthetic implied-volatility surfaces, a 69.9% no-arbitrage filter, a real SPY OOD stress test, and three calibration pipelines—supervised MLP, unsupervised BSDE, and differentiable surface-matching. Episode 5 of my thesis study series (Chapter 4a). Mechanisms and design choices first; full scorecards come in Episode 6. What you’ll learn • GPU Monte Carlo synthetic dataset design for rough Bergomi • Why ~70% of draws are rejected (calendar & butterfly no-arbitrage) • How filter bias under-trains the empirically relevant low-H region • Fixed forward variance ξ₀ = 0.04 and why real SPY sits out-of-distribution • EDA takeaways: parameters, surfaces, and SPY vs training distribution • Pipeline 1: supervised surface → parameter MLP • Pipeline 2: label-free BSDE pricing/hedging loop • Pipeline 3: differentiable surface-matching (4 key tricks: prices not IVs, CRN, sigmoid reparam, restarts) • Why surface-matching exists as a supervised-independent parameter route Series: Rough Volatility Calibration with Physics-Informed Neural Networks Episode 5 of 7 · Chapter 4a — Data & pipelines Next: Ep.6 — Results, SPY stress test, and why Hurst H is hardest to recover Topics: implied volatility surface, synthetic data, no-arbitrage, rough Bergomi, neural network calibration, BSDE, differentiable calibration, SPY options, quantitative finance experiments #ImpliedVolatility #RoughBergomi #DeepLearning #QuantFinance #DataScience