The core idea
A volatility smile is not a clean curve until you make it one.
Exchange data arrives as discrete strikes, expiries, bid/ask levels, trades, and sometimes stale markets. SVI gives each expiry a stable mathematical shape, so a system can evaluate volatility between listed strikes rather than jumping from quote to quote.
Normalize strikes
Convert strike space into log-moneyness, k = ln(K / F), so every quote is measured relative to the forward.
Fit total variance
Calibrate total implied variance, w = IV^2 x time, rather than raw volatility points.
Publish diagnostics
Ship the fitted smile with quote quality, residuals, stability checks, and surface context.
SVI is the shape of the smile. A production volatility surface is the full pipeline around it: quote cleaning, forward context, calibration, constraints, diagnostics, and live monitoring.
Formula
The five raw SVI parameters map to level, skew, wings, center, and curvature.
Raw SVI fits total implied variance, w(k), against log-moneyness, k = ln(K / F). The result is the expiry slice used for interpolation, risk reversals, flies, and surface monitoring.
Total implied variance
The fitted target, usually IV squared times time to expiry.
Log-moneyness
k = ln(K / F), so strikes are measured relative to the forward.
Strike
The listed option strike being converted into log-moneyness.
Forward
The expiry-matched forward level used as the smile center reference.
Time to expiry
The year fraction used when converting implied volatility into total variance.
Vertical level
Raises or lowers the total-variance smile. In calibration it works with the wing term and must leave the fitted variance non-negative.
Wing scale
Sets the overall steepness of the smile wings. Together with rho, it determines the left and right asymptotic slopes.
Skew rotation
Rotates the smile and redistributes slope between put and call wings. Negative rho usually makes the downside wing steeper.
Horizontal displacement
Moves the center of the smile along the log-moneyness axis. Increasing m shifts the fitted curve to the right.
Body smoothness
Controls the rounding near the smile center. Larger sigma reduces local curvature around the body of the market.
Worked example
How a BTC option quote becomes one point in the fit.
Suppose a 30-day BTC forward is 80,000 and a 72,000 strike is marked around 54% implied volatility. SVI does not fit that as a raw strike-volatility pair. It first puts the quote on the same coordinate system as the rest of the expiry.
Pass near liquid mids without overreacting to outliers.
Price intermediate strikes and derive 25-delta RR/fly metrics.
Screenshots
Fitted smiles, risk nodes, and diagnostics stay visible together.
The dashboard is designed around the reality that the formula is only half the problem. Traders need to see the fit, the derived risk nodes, and whether the surface is behaving across tenors.
Engineering deep dive
Engineering a real-time BTC options volatility surface.
Sean Gordon's LinkedIn article gives the implementation view: live BTC options data, surface construction, SVI fitting, and the production details behind real-time implied volatility analytics.
Read the engineering articleProduction checks
The guardrails matter as much as the curve.
A visually smooth smile can still be wrong. Real-time crypto surfaces need checks that separate genuine market structure from stale quotes, one-off prints, and unstable parameter jumps.
Quote quality
Filter stale, crossed, or structurally wide markets before they dominate a fit.
Butterfly sanity
Check local curve shapes that can imply impossible density inside one expiry slice.
Calendar sanity
Watch whether total variance behaves consistently across neighboring expiries.
Parameter stability
Flag jumps where the fitted smile moves more than the quote set justifies.
API access
SVI surface data is available for testing by request.
Derivasys can expose fitted surfaces through WebSocket streams and REST endpoints for approved testers. The API boundary covers live snapshots, incremental patches, smile levels, diagnostics, risk nodes, and fixed-tenor rows.
- Live surface snapshots and sparse WebSocket patches
- Current-state REST responses for smiles, diagnostics, and risk nodes
- Fixed-tenor rows alongside native expiry views
- BTC and ETH surfaces, with additional altcoin feeds under testing
FAQ
Common questions about SVI.
What does SVI mean in options volatility?
SVI stands for Stochastic Volatility Inspired. It is a parametric model for fitting implied total variance as a function of log-moneyness.
Is SVI a pricing model?
No. SVI describes the volatility smile. Pricing still needs forwards, option conventions, discounting assumptions, and a clean calibration workflow.
Why use SVI instead of interpolation?
Interpolation connects known quotes. SVI adds a compact shape with level, skew, wing, center, and curvature controls, which makes monitoring and risk extraction cleaner.
Does SVI work for BTC and ETH options?
Yes, provided the surrounding data pipeline is robust. BTC and ETH options often have uneven strike liquidity and visible skew, which is where a stable smile fit is useful.
References
Primary source and related Derivasys pages.
The guide is written for practitioners, but the model is grounded in SVI literature and the Derivasys production workflow.
Next guide
Sticky strike vs sticky delta.
The next step after fitting the smile is understanding what should stay fixed when the forward moves: the listed strike or the delta bucket.
Read the convention guide