Raw SVI¶
Overview¶
The original Gatheral (2004) parametrization with 5 free parameters per slice. Maximum flexibility; the workhorse for liquid equity smiles.
Model¶
\[w(k) = a + b\left[\rho(k - m) + \sqrt{(k - m)^2 + \sigma^2}\right]\]
Parameters¶
Parameter |
Meaning |
Constraint |
|---|---|---|
\(a\) |
overall variance level |
\(a \geq 0\) |
\(b\) |
slope / curvature scale |
\(b > 0\) |
\(\rho\) |
skew (correlation) |
\(|\rho| < 1\) |
\(m\) |
log-moneyness shift |
unconstrained |
\(\sigma\) |
vol-of-vol (smile width) |
\(\sigma > 0\) |
Usage¶
from pysvi import get_model, calibrate_slice
model = get_model("svi")
params = calibrate_slice(df_slice, model)
# params: {'a', 'b', 'rho', 'm', 'sigma', 'forward'}
No extra keyword arguments are required.
Arbitrage behaviour¶
No automatic arbitrage guarantees beyond soft parameter bounds (QUASI). Combine with NO_BUTTERFLY and/or NO_CALENDAR for penalty-based enforcement — see Arbitrage freeness.
References¶
Gatheral, J. (2004). “A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives.”