Dual Delta
Canonical definition, formula, interpretation, and API reference.
Definition
Sensitivity of option price to strike price. Approximates the risk-neutral probability of finishing ITM.
Formula
Dual Delta = dV/dK = -e^(-rT) x N(d2) for calls
Derivative of option value with respect to strike price.
Inputs
spotstrikeimplied voltime
Output
dual delta value
Interpretation
- Negative for calls (higher strike = lower call value)
- Absolute value approximates risk-neutral ITM probability
- Positive for puts
API Reference
Endpoint
GET /v1/pricing/greeks
Tier
Free
Response field
second_order.dual_delta
Why Dual Delta Matters for Trading
TL;DR
Dual delta is the option's sensitivity to the strike itself. Quant tool — used for strike selection, synthetic replication, and exotic pricing.
- What it measures
- ∂V/∂K — how option value changes as the strike is shifted.
- What it signals
- Sensitivity across strike space rather than spot space.
- Why we measure it
- Dual delta is the bridge from single-option pricing to multi-strike structures (digitals, one-touches, replicated payoffs).
- Who uses it
- Quants, structured-products desks, market makers.
How to read Dual Delta
High dual delta
- Structure very strike-sensitive
- Digital-option replication
- Fine-grained strike tuning
- Common in exotic books
Good for: structured-product desks
Near-the-money at expiry
- Discontinuous at expiry
- Model instability
- Replication breaks down
- Avoid for settlement-close trades
Bad for: expiry-settled strategies
Deep ITM / OTM
- Dual delta stable
- Predictable behaviour
- Normal strike-selection regime
- Retail-accessible
Stable
Rules of thumb
- Quant territory. Most retail traders never touch dual delta — ATM-adjacent options don't expose you to it meaningfully.
- Goes discontinuous at expiry ATM. Model blow-ups at the strike boundary. Don't rely on it for settlement-close exposure.
- Used in digital replication. Digitals are synthesised from tight call spreads — dual delta is the math.
- Pair with delta. Dual delta complements spot delta — both are first-order sensitivities, just in different variables.
- Stable away from ATM. Deep ITM/OTM dual delta behaves well; use freely.
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