Ultima
Canonical definition, formula, interpretation, and API reference.
Definition
Third derivative of option value with respect to implied volatility. How vomma changes with vol.
Formula
Ultima = d³V/dσ³
Third-order vol sensitivity. Measures curvature of vega convexity.
Inputs
vommaimplied vol
Output
ultima value
Interpretation
- Relevant for exotic vol-of-vol strategies
- Large ultima = highly nonlinear vol sensitivity
- Typically small for vanilla ATM options
API Reference
Endpoint
GET /v1/pricing/greeks
Tier
Free
Response field
third_order.ultima
Why Ultima Matters for Trading
TL;DR
Ultima is third-order vega - vomma's convexity. Tail-risk and vol-of-vol quant territory.
- What it measures
- ∂Vomma/∂σ - third derivative of option value w.r.t. vol.
- What it signals
- How vomma itself changes as vol moves.
- Why we measure it
- At the deep tails, vol is path-dependent. Ultima captures the non-linearity second-order vega misses.
- Who uses it
- Vol quants, VIX-option traders, tail-risk desks.
How to read Ultima
Long ultima (deep OTM / VIX calls)
- Convex-on-convex vol payoff
- Profits in vol-regime shifts
- Tail-event captures
- VIX-call bread and butter
Good for: tail hedges, VIX longs
Short ultima (naked wing sells)
- Convex-on-convex losses in vol shocks
- Tail-event blow-ups
- Short-vol wing exposure
- VIX events destroy
Bad for: short tail sellers
ATM / normal regimes
- Ultima ≈ 0
- Not a retail concern
- Managed through vega hedging
- Background noise
Flat
Rules of thumb
- Tail-only Greek. Ultima matters deep OTM during vol regime shifts. Elsewhere it's zero.
- Pair with vomma. Ultima is vomma's convexity - a pure meta-Greek.
- Quant desks only. Managed by quants, rarely understood by retail.
- Event-dependent P&L. Ultima P&L is zero on calm days, dominant during regime shifts.
- Structural hedge tool. Long-ultima VIX calls are the backbone of many tail-risk programs.
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