The core idea
Traders observe option prices at discrete strikes, with noisy bid, ask, and last-trade updates. Those quotes imply a smile, but not a continuous function. SVI turns that scattered information into a smooth parametric curve that can be evaluated consistently across strikes.
In practice, SVI is usually written in terms of total implied variance w(k) against log-moneyness k. A common raw form is:
w(k) = a + b * ( rho * (k - m) + sqrt((k - m)^2 + sigma^2) )
The parameters control level, slope, curvature, skew orientation, and the horizontal location of the smile. By calibrating those parameters separately for each expiry, a system can construct a continuous volatility surface rather than relying on sparse point-in-time quotes.
Why total variance instead of volatility
Fitting directly in total variance makes the model easier to work with mathematically and helps comparisons across expiries. It also aligns with how arbitrage conditions are commonly checked in surface construction.
Where SVI shows up in a real workflow
- Fitting per-expiry option smiles from live market quotes
- Building smooth surfaces for valuation and risk reporting
- Extracting risk reversal and fly nodes from a fitted curve
- Monitoring dislocations between quoted markets and fitted mids
- Comparing venue-specific quotes against a normalized surface
What SVI does not do on its own
SVI is a parameterization, not an entire pricing stack. It still depends on data cleaning, forward estimation, quote selection, calibration constraints, and diagnostics. A good live surface is not just the formula, it is the full methodology around the fit.