SABR vs Heston

Side-by-Side

When to Use SABR

• Per-expiration smile fit. If you need to fit a single expiration's smile compactly with minimal calibration overhead, SABR with the Hagan formula is the practitioner standard. The 4 parameters capture the typical smile shape across liquid strikes; pricing each strike uses an analytical closed-form approximation.
• Interest-rate options. SABR is the industry standard for caplets, floorlets, and swaptions. The β parameter (which interpolates between normal-distribution dynamics at β=0 and lognormal at β=1) is essential for rates products where the choice of underlying-process character is regime-dependent.
• Speed-critical pricing. SABR's closed-form Hagan approximation runs at microsecond speeds, making it practical for real-time market-making and high-frequency vol-arbitrage strategies. Heston's FFT pricing, while fast, is 10-100x slower.
• Smile interpolation between listed strikes. When you need to price a non-listed strike (off-the-grid), SABR's Hagan approximation provides a smooth interpolation between liquid strikes. Note that the Hagan formula is an asymptotic approximation and is not automatically arbitrage-free across all parameter ranges, particularly in the wings; production systems typically pair it with no-arbitrage corrections (Lee's moment formulas, normal SABR for low strikes).
• Quick recalibration. SABR calibrates in milliseconds per expiration. Useful in market-making contexts where the surface needs to be refit thousands of times per second.

When to Use Heston

• Full-surface consistency. When you need a single model that prices all expirations consistently with shared parameters, Heston is preferred. The mean-reversion structure (κ, θ) explicitly generates term structure, so calibration produces a single set of parameters that fits the entire surface.
• Forward-vol modeling. Cliquets, forward-start options, variance swaps, and any product depending on the smile at a future date requires Heston-class models. SABR doesn't have a clean forward-smile generation mechanism.
• Long-dated options. Mean reversion of variance is essential for accurately pricing options 1+ years out. Heston explicitly models the convergence of variance toward θ; SABR fits per-expiration without this dynamic.
• Vol-of-vol products. VIX options, VVIX, and variance-of-variance products require explicit modeling of vol-of-vol. Heston's ν parameter has a direct economic interpretation as variance-of-variance.
• Risk-neutral density extraction. Heston produces well-defined risk-neutral densities at every horizon; SABR is more typically used for smile fitting at fixed expirations rather than density modeling.

Where They Agree

Both produce equivalent quality of fit on a single expiration's smile in most regimes. For SPX 30-day smile, both calibrate to within 0.1-0.2 vol points of listed prices. The ρ parameter has the same interpretation in both: correlation between spot returns and stochastic-vol increments.

Both are stochastic-volatility models in the sense that variance follows its own driving Brownian motion. Both produce skew through ρ and smile curvature through their vol-of-vol parameters (ν in both cases, despite the different overall parameterizations).

Where They Diverge

• Term structure consistency. SABR fit to 30 DTE and 60 DTE separately may produce parameter sets that imply inconsistent forward dynamics between them. Heston calibrated to the full surface enforces a single set of parameters that is consistent across expirations by construction.
• Computational tradeoffs. SABR pricing is dramatically faster per option but requires calibration per expiration. Heston pricing is slower per option but requires only a single calibration for the entire surface. The crossover point depends on how many expirations and how often you need to recalibrate.
• Exotic option pricing. Path-dependent exotics (Asian, barrier, forward-start, cliquet) generally require Heston-class models for consistent pricing. SABR is typically used only for European options at fixed expirations.
• The β parameter. SABR has β; Heston does not. β allows SABR to interpolate between normal and lognormal dynamics, which matters specifically for low-rate regimes (β=0 produces normal vol; β=1 produces lognormal). Heston is locked to lognormal-equivalent spot dynamics with stochastic vol overlay.

Why They're Often Confused

Both are stochastic-volatility models that capture skew via ρ and smile via ν. The architectural difference (per-expiration smile fit vs full-surface dynamic model) gets lost in the shared "SV model" categorization. In practice, large institutional vol desks run both: SABR for fast smile interpolation and IR products; Heston for surface-consistent pricing and forward-vol-sensitive exotics.

The β parameter is what distinguishes SABR most sharply from Heston conceptually. Heston implicitly has a fixed underlying process character (close to lognormal with vol scaling); SABR lets you choose. This is why SABR dominates rates pricing where the underlying process character matters more than in equities.

Further Reading

• SABR Model Documentation
• Heston Model Documentation
• Pricing Model Landscape
• What Is Volatility Skew?
• What Is Vol of Vol?
• Heston vs Black-Scholes

References

• Hagan, P. S., Kumar, D., Lesniewski, A. S., and Woodward, D. E. (2002). "Managing Smile Risk." Wilmott, 1, 84-108.
• Heston, S. L. (1993). "A Closed-Form Solution for Options with Stochastic Volatility..." Review of Financial Studies, 6(2), 327-343.
• Gatheral, J. (2006). The Volatility Surface. Wiley. Chapters 5 (SABR) and 3 (Heston).

This is one of the model-vs-model comparison pages. For the full landscape of pricing models and their relationships, see the Pricing Model Landscape.