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.

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.

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.

Models vs Methods - Conceptual Overview

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

Models vs Methods: A Conceptual Overview

Why This Matters

Key insight: Options pricing involves two distinct components working together: a model that describes how prices move, and a method that computes the option value.

Practical example: When you select "Heston + FFT" in this calculator, you're choosing the Heston stochastic volatility model (the dynamics) solved via Fast Fourier Transform (the computation method).

Understanding the difference between pricing models and numerical methods is fundamental to using options calculators effectively. Many users conflate these concepts, but they serve distinct purposes in the pricing pipeline.

What Is a Pricing Model?

A pricing model defines the assumptions about how the underlying asset price evolves over time. It specifies the stochastic process (the mathematical description of random price movements) and determines what factors drive option value.

The model answers questions like: Is volatility constant or does it change? Can prices jump discontinuously? How does volatility correlate with price movements?

Model	Price Dynamics	Key Assumption	Best For
Black-Scholes	Geometric Brownian Motion	Constant volatility	Liquid vanilla options, baseline pricing
Heston	GBM + mean-reverting stochastic vol	Volatility follows its own random process	Volatility smile/skew, longer-dated options
SABR	Stochastic vol with CEV backbone	Vol correlated with forward rate	Interest rate options, FX, smile fitting
Merton Jump Diffusion	GBM + Poisson jumps	Prices can jump discontinuously	Earnings events, crash risk, fat tails
Variance Gamma	Pure jump process (no diffusion)	Price changes arrive at random times	Heavy tails, short-dated options
Local Volatility	GBM with state-dependent vol	Vol is a deterministic function of S and t	Exact market calibration, exotic pricing

What Is a Numerical Method?

A numerical method is the computational technique used to solve the pricing equations that arise from a given model. Once you've chosen a model (the "what"), the method determines "how" you compute the option price.

Some models have closed-form analytical solutions (like Black-Scholes for European options), but most real-world pricing requires numerical approximation.

Method	How It Works	Strengths	Best For
Analytical	Closed-form mathematical formula	Instant computation, exact (when available)	European vanilla under BS, Greeks
Binomial/Trinomial Trees	Discretize time and price into a lattice	Handles early exercise, intuitive	American options, dividend modeling
Monte Carlo	Simulate thousands of random price paths	Handles any payoff, any model	Path-dependent, multi-asset, complex payoffs
FFT (Fourier Transform)	Invert the characteristic function	Very fast for models with known char. function	Heston, Variance Gamma, model calibration
PDE (Finite Difference)	Solve the pricing PDE on a discrete grid	Accurate, handles boundaries well	American options, barriers, local vol

How Models and Methods Combine

In principle, any model can be solved by any method, but certain combinations are more natural and efficient. The choice depends on the option type, required accuracy, and computational constraints.

Combination	Why It Works	Typical Use Case
Black-Scholes + Analytical	BS has a closed-form solution	Instant vanilla pricing, IV calculation
Black-Scholes + Binomial	Lattice handles early exercise	American options on dividend stocks
Heston + FFT	Heston has known characteristic function	Fast smile calibration, volatility surface
Any Model + Monte Carlo	MC is model-agnostic via simulation	Complex path-dependent payoffs, multi-asset
Local Vol + PDE	PDE naturally handles variable coefficients	Barrier options, American under local vol
Jump Models + FFT	Jump processes have tractable char. functions	Variance Gamma pricing, Merton model

Practical Implications

Model mismatch matters more than method accuracy: Using the wrong model (e.g., Black-Scholes when there's significant skew) introduces far more error than choosing between FFT vs Monte Carlo.
Methods converge to the same answer: For European options under the same model, Binomial, Monte Carlo, FFT, and PDE all converge to the same price with sufficient precision.
American options require appropriate methods: Analytical solutions rarely exist; use Binomial trees or PDE for early exercise features.
Speed vs accuracy tradeoff: Analytical and FFT are fastest; Monte Carlo is most flexible but slower; PDE offers a balance for American-style products.

What About Exotic Options?

Note: The 7 exotic option types in this calculator (Asian, Barrier, Lookback, Digital, Compound, Chooser, Multi-Asset) are neither pricing models nor numerical methods. They are payoff structures that define what you're pricing.

The complete pricing pipeline is: Option Type (the payoff) + Model (the dynamics) + Method (the computation) = Price. For example, pricing an Asian option under Heston dynamics using Monte Carlo simulation.

Exotic options often require specific numerical methods due to their path-dependent or complex payoff structures. Monte Carlo is particularly well-suited for most exotics because it can handle arbitrary payoff definitions through simulation.

For detailed documentation on each model and method, see the individual sections below.

This page is part of the Options Analysis Suite documentation hub. Browse the glossary for term definitions.