Why do different models give different prices?

Each model embeds different assumptions about the underlying dynamics (constant vol, stochastic vol, jumps, surface fitting). All can match the listed surface at calibration, but they disagree on non-listed strikes, future evolution, and exotic payoffs.

How do traders use model divergence?

Persistent gaps between Heston, SABR, and local-vol prices on the same contract signal where model risk is concentrated. Hedging desks use the spread to size model-uncertainty reserves and avoid pricing errors on illiquid strikes.

Which model is correct?

No single model is correct everywhere. Heston captures stochastic volatility but misses short-dated smile dynamics; SABR fits per-expiry smiles well but lacks a coherent term structure; local-vol fits the surface perfectly but has unrealistic forward-vol dynamics.

When does model divergence widen?

During regime transitions (low-vol to high-vol environments), around binary events, and in illiquid surfaces where the listed price is not a clean reference. Convergent calibrations indicate a stable, well-priced market.

What Is Model Divergence?

Q: What is model divergence?

Model divergence is the dispersion of prices (or fitted IVs) produced by different calibrated pricing models for the same option contract. The gap measures priced uncertainty about which model best describes the current regime.

Last reviewed: May 17, 2026 by Options Analysis Suite Research.

Model divergence is the dispersion of prices (or fitted implied volatilities) produced by different calibrated pricing models when applied to the same option contract. The Black-Scholes price for an OTM put is rarely identical to the Heston price, the SABR price, the Jump-Diffusion price, or the Local-Volatility price. The size and direction of those differences is itself priced information about regime structure.

Why Do Models Disagree?

Each pricing model makes different structural assumptions. Where the assumptions matter empirically (skew, smile, jumps, mean reversion), models produce different prices. Where the assumptions are roughly equivalent (ATM strikes in calm regimes), models converge. The pattern of agreement and disagreement across the surface reveals which features are doing work in the current regime.

Constant vs stochastic volatility. Black-Scholes prices every strike with the same sigma; Heston, SABR, and Local Vol allow vol to vary. Smile-aware models price OTM strikes differently from BS by an amount that grows with how much smile is in the surface.
Continuous vs jump dynamics. Black-Scholes and Heston have continuous price paths; Merton, Kou, Bates, and Variance Gamma allow discontinuous moves. Around earnings, around Fed days, and on names with high jump-event frequency, the jump models materially diverge from the continuous family.
Path-dependent vs path-independent fits. Local Volatility fits today's surface exactly but distorts forward dynamics; Heston and SABR sacrifice some surface accuracy for cleaner forward dynamics. The two families disagree on barriers, cliquets, and any forward-skew-dependent payoff.
Calibration scope. SABR fits per-expiration; Heston fits joint surfaces; Local Vol fits everything by construction. Different calibration scopes produce different residual error patterns.

Reading Divergence

Small divergence on ATM strikes: typical and expected. ATM is where the smile is anchored and most models agree to within a small tolerance.
Large divergence on OTM strikes: the smile is doing work. Black-Scholes is missing the wing premium that Heston, SABR, and Variance Gamma include.
Large divergence on short tenors: jumps are doing work. The continuous models under-price the gap risk that jump-aware models capture.
Cross-tenor divergence shifts: term-structure dynamics are doing work. SABR per-expiration vs Heston joint-fit will disagree where the joint constraint binds.

How Do Pricing Models Bridge to Divergence?

Black-Scholes as the reference frame. All other models are typically expressed as deviations from BS. The BS-implied IV difference between two model prices is the cleanest universal measure of disagreement.
Heston vs Black-Scholes: loads primarily on stochastic volatility and surface curvature that constant-vol cannot represent.
Jump diffusion (Merton, Kou) vs Black-Scholes: loads primarily on jump-risk premium, the price the market pays for sudden discrete moves.
Variance Gamma vs Black-Scholes: loads on tail heaviness and asymmetry beyond what lognormality accommodates.
Heston vs Merton: the most diagnostic pairing for tail-risk regime. Isolates whether the market expects grinding vol expansion (Heston's world) or sudden discrete repricing (Merton's world).
SABR vs Heston: SABR per-expiration vs Heston joint-surface. Disagreement reveals where term-structure consistency is binding the joint fit.
Local Volatility vs Heston: exact static fit vs realistic forward dynamics. Disagreement on path-dependent payoffs reveals how much forward-vol structure matters.

The Regime-Detection Application

Cross-model divergence is the foundation of the platform's regime-detection screener. Eight calibrated models (Black-Scholes, Heston, SABR, Local Volatility, Merton, Kou, Bates, Variance Gamma) each produce a fit error against the listed surface. The median absolute deviation of those fit errors, normalized by the median, produces a dispersion score.

Three distinct signals emerge from the dispersion structure:

High dispersion + low median error: some models are fitting well, others are not. The surface has feature richness (jumps, stochastic vol, fat tails) that only specific model classes capture. Regime is feature-driven.
Low dispersion + low median error: all models agree closely. Surface is clean and any standard model handles it. Regime is calm.
Low dispersion + high median error: all models fit poorly. No standard model handles the regime. This is the rarest and most diagnostic signal: a surface that is structurally hard to fit.

Why Does This Concept Matter?

Divergence is not a directional trade signal. It is a structural diagnostic. The trade implication is contingent: if BS is significantly cheaper than the jump-diffusion price on a front-month OTM put two weeks before earnings, the market is paying a jump premium for the event. Whether you trade depends on whether you think the priced jump premium is rich, fair, or cheap relative to your forecast.
Divergence reveals which features are priced. When Heston fits well but Local Volatility fits poorly on a specific name, the market is pricing forward-vol dynamics that the static surface cannot represent. That is information about which model class to use for that ticker.
Cross-model triangulation isolates risk premia. The premium for jump risk is approximately the price difference between a jump-aware model and a continuous model on the same option. The premium for stochastic vol risk is approximately the difference between a stochastic-vol model and a constant-vol model. These decompositions are operational, not just theoretical.

Related Concepts

Pricing Model Landscape · Options Market-Structure Ontology · Heston vs Black-Scholes · SABR vs Heston · Volatility Skew · Tail Risk · Vol of Vol

References & Further Reading

Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley. The reference text on cross-model surface comparison.
Carr, P. and Wu, L. (2003). "What Type of Process Underlies Options? A Simple Robust Test." Journal of Finance, 58(6), 2581-2610. Empirical decomposition of jump vs diffusion components.
Bates, D. S. (1996). "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options." Review of Financial Studies, 9(1), 69-107. The Bates model combines stochastic vol with spot jumps.
Bollerslev, T. and Todorov, V. (2011). "Tails, Fears, and Risk Premia." Journal of Finance, 66(6), 2165-2211. Cross-model decomposition of priced tail risk.

View live model-divergence screener (cross-model dispersion ranked by ticker) ->

This page is part of the Pricing Model Landscape and the canonical reference set on options market structure. Browse all documentation.

As of the latest snapshot, AAPL has an ATM implied volatility of 21.6%, IV rank 28% (percentile 13%); 20-day realized vol 25.9%. 25-delta skew is +1.6%, meaning OTM puts trade richer than OTM calls. The IV here is the input that pricing-model walkthroughs (Black-Scholes, Heston, SABR, local-vol) take as their starting point: each model decomposes the same observed quote into different latent dynamics (constant vol, stochastic vol, surface-fitted vol, etc.) which is why two models can agree on price but disagree on Greeks and on how vol will evolve.