Why do different options pricing models give different prices for the same option?

Each model makes different assumptions about how the underlying moves. Black-Scholes assumes constant volatility and continuous paths, producing a single fair value per option. Heston adds stochastic volatility, capturing the smile that Black-Scholes can't reproduce. Jump-diffusion models (Merton, Kou, Bates) add discontinuous price jumps for event risk. Variance Gamma uses pure-jump Lévy dynamics with explicit fat tails. Local Volatility fits the listed surface exactly by construction. The 'correct' price depends on which assumptions best match the underlying's actual dynamics, and the gap between two models is itself priced information about which assumptions the market is paying for.

When should I trust the model prices from an options calculator?

Model prices are most reliable for liquid, near-ATM options with 20-60 days to expiration on optionable underlyings with continuous trading and well-defined dividend schedules. Trust degrades for: (a) illiquid options where bid-ask spreads exceed 10% of mid, (b) deep OTM strikes where the smile dominates and model choice matters most, (c) options under one week to expiration where pin risk and discrete dividend effects can dominate, (d) options on underlyings during major events (earnings, FDA, FOMC) where jump risk needs an explicit jump model. The platform's model-divergence view shows where models disagree, which flags the cases that need extra caution.

Which pricing model should I use for which situation?

Black-Scholes for fast pre-trade pricing, IV computation, and as the reference for divergence checks. Heston for surface-aware pricing where the smile and term structure matter jointly. SABR for fitting per-expiration smiles cleanly. Local Volatility when you need calibration-perfect repricing of the listed surface. Jump-diffusion (Merton, Kou, Bates) for options around earnings or known event jumps. Variance Gamma for fat-tailed Lévy returns. Binomial trees or PDE for American-exercise pricing. Monte Carlo for path-dependent exotics and risk-neutral probability distributions. The platform exposes all of these so you can compare.

Which model best handles options around earnings?

Around earnings the front-month tenor concentrates jump risk that continuous models (Black-Scholes, Heston, Local Vol) systematically under-price. The right tools are jump-diffusion variants: Merton for symmetric jumps, Kou for asymmetric (downside-skewed) jumps, Bates for jumps plus stochastic volatility. The model divergence between Black-Scholes and Bates on a front-month ATM straddle is roughly the jump premium the market is paying for the event. After the event, the front-month IV typically collapses (IV crush); the post-event jump premium effectively goes to zero, and Black-Scholes regains accuracy.

How does model calibration to the listed surface work?

Calibration finds the model parameters that minimize the squared error between model-computed prices and listed market prices across a chosen strike-tenor grid. For Heston, the five parameters (κ, θ, ξ, ρ, v₀) are jointly fit; for SABR, the three parameters (α, ρ, ν, with β fixed) are fit per-expiration. The optimization is typically Levenberg-Marquardt on the log-IV space (more stable than fitting prices directly). The platform calibrates daily after market close and exposes the resulting parameter sets, the residual error per option, and the implied IV surface from the calibrated model; this lets users see where each model is fitting and where it's straining.

What Is Model Divergence?

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 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 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 This Concept Matters

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 · 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..." Review of Financial Studies, 9(1), 69-107. The Bates SVCJ model that combines stochastic vol with 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.