Question 1

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

Accepted Answer

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.

Question 2

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

Accepted Answer

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.

Question 3

Which pricing model should I use for which situation?

Accepted Answer

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.

Question 4

Why are American and European option prices sometimes identical and sometimes not?

Accepted Answer

For a call on a non-dividend-paying stock, early exercise is never optimal (you'd give up remaining time value to capture only intrinsic value) so American = European. The two prices diverge when (a) the option is a put (early exercise of an ITM put recovers the strike's interest, especially when rates are positive), (b) the stock pays dividends large enough that exercising the call before ex-dividend captures more than the time value left, or (c) the option is deep ITM with significant rate or carry differentials. The early-exercise premium is what the binomial tree and PDE methods compute.

Question 5

How does model calibration to the listed surface work?

Accepted Answer

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.

Question 6

Which model best handles options around earnings?

Accepted Answer

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.

Pricing Models: 17 Options Pricing Models

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