DerivasysReportsDashboard

By Sean Gordon / Published / Updated

Model guide

What is rough volatility?

Rough volatility models treat instantaneous variance as substantially less smooth than Brownian motion. The practical question is whether that roughness produces more realistic volatility dynamics without disguising event premium or calibration instability.

Roughness / forward variance / rough Bergomi / calibration limitations.

Read the Derivasys studyImplied surface guide

Mechanism

The Hurst parameter describes memory and path roughness.

Brownian motion has H equal to one half. Fractional processes with H below one half have negatively correlated increments: an upward variance move is more likely to be followed by a downward increment, and vice versa. The path remains continuous but looks jagged at every resolution.

That property is not the same as high volatility of volatility. H controls temporal texture; eta controls amplitude. A calibration that drives both toward extreme bounds is a diagnostic to investigate, not a reason to extrapolate the model without limits.

Rough Bergomi

Rough Bergomi adds stochastic rough dynamics to a forward-variance curve.

The model starts from ξ₀(t), the market's forward-variance curve, then evolves that curve with a fractional kernel. Correlation between spot and variance shocks creates skew, while eta and H shape how volatility risk moves across horizons.

H / Hurst parameter

Controls path roughness. Values below one half produce negatively correlated volatility increments; empirical rough-volatility work commonly estimates H well below one half.

η / Volatility of volatility

Controls how strongly the variance process moves. A high fitted eta can be genuine dynamics, a compensation for a misspecified forward-variance curve, or a parameter-bound warning.

ρ / Spot/volatility correlation

Controls the signed leverage response and much of the model smile's skew. Negative rho normally raises downside implied volatility relative to upside volatility.

ξ₀(t) / Forward variance curve

Anchors the expected variance term structure. It must be aligned with the source implied surface before H, eta or rho can be interpreted.

Relationship to implied volatility

An implied surface is a market snapshot; rough volatility is a model of dynamics.

SVI or SSVI parameterises option-implied total variance across strike and maturity. Rough Bergomi instead specifies how variance and spot can evolve. A calibration uses the implied surface as a target, but a low fitting error does not prove that the dynamics are correct.

For Derivasys, the clean separation is: use accepted SVI state as the observable market input, use rough volatility only for an explicitly labelled scenario or research layer, and preserve the source-surface identifier with every result.

Calibration

Parameter stability and out-of-sample behavior matter more than one residual score.

  1. Freeze and identify the source surface, conventions and interpolation grid.
  2. Infer a defensible forward-variance curve before fitting roughness or correlation.
  3. Use common random numbers and a fixed seed when comparing parameter candidates.
  4. Record bounds, objective, optimiser, path count and time grid.
  5. Test short-tenor and later-snapshot behavior separately from the calibration sample.

Failure modes

Roughness is not a universal explanation for the surface.

  • A rough diffusion does not automatically explain event premium, jumps or near-expiry market microstructure.
  • Different parameter combinations can generate similar option prices, so calibration stability matters as much as in-sample error.
  • Monte Carlo noise can look like smile structure unless paths, seeds and time discretisation are controlled.
  • A fit to one frozen surface does not establish out-of-sample dynamics or production readiness.
  • Static-arbitrage checks still apply to any implied surface generated from the model.

Derivasys research

The frozen-snapshot experiment is published separately from this primer.

The Derivasys study tests a medium/long rough-volatility backbone against one identified SVI snapshot, documents the failed short-tenor implication, compares overlay candidates and exposes a reproducibility manifest and results table.

Inspect the rough-volatility scenario study and artifacts

References and related reading

Continue from model definition to surface evidence.