version: "1.0.1" name: fit-volatility-smile description: Fit an implied-volatility smile (SVI / SABR / quadratic) to option-chain IVs across log-moneyness using alphavar, and query the fitted IV plus a no-arbitrage (butterfly) check. Use when a user asks to fit/parametrize a vol smile or surface slice, interpolate/extrapolate IV across strikes, or check a smile for butterfly arbitrage. when_to_use: Use when a user asks to fit/parametrize a vol smile or surface slice, interpolate/extrapolate IV across strikes, or check a smile for butterfly arbitrage. metadata: owner: alphavar

Fit a volatility smile with alphavar

USAGE skill (concept → function → how to apply). Verified against src/ — re-confirm the API before relying on it; the public surface drifts.

Concept

A volatility smile is the implied volatility as a function of strike (here, log-moneyness k = ln(K / F)) for a single expiry. A parametrization (SVI, SABR, a quadratic) fits a smooth curve to observed IVs so you can interpolate/extrapolate IV at any strike and test the slice for butterfly (static) no-arbitrage.

Implementing function

alphavar.options.lib.pricer.smile:

• make_smile_model(name) → a SmileModel (name ∈ SMILE_MODELS; default

DEFAULT_SMILE_MODEL = SVI). Or use the classes directly: SVISmile, SABRSmile, QuadraticSmile.

• SmileModel.fit(k, iv, t_years, weights=None) → a `SmileResult`.
• SmileResult.iv(k) — fitted IV at log-moneyness k; .total_variance(k);

.is_butterfly_free(k_grid=None, tol=-1e-6) — numeric no-arbitrage check.

The DataFrame-level driver (fit per expiry over a chain) lives in alphavar.options.lib.pricer._smile_enrich.

Inputs & conventions

• `k` — log-moneyness ln(K/F) (a numpy array), not raw strike.
• `iv` — implied vols at those k (decimals, e.g. 0.62, not 62).
• `t_years` — time to expiry in years.
• `weights` — optional per-point weights (e.g. by liquidity).

Failure modes

• Too few points / degenerate slice → fit raises or returns a poor result; check

is_butterfly_free() before trusting it.

• A fit can succeed numerically yet be arbitrageable — always run the butterfly check.
• iv in percent instead of decimals is the most common silent error.

Example

import numpy as np
from alphavar.options.lib.pricer.smile import make_smile_model
k  = np.array([-0.20, -0.10, 0.0, 0.10, 0.20])   # log-moneyness
iv = np.array([0.72, 0.65, 0.60, 0.63, 0.69])    # implied vols (decimals)
model = make_smile_model("svi")                  # or SVISmile(); default is SVI
res = model.fit(k, iv, t_years=0.25)
res.iv(np.array([-0.05, 0.05]))                  # interpolated IV at new strikes
res.is_butterfly_free()                          # True if static no-arbitrage holds

For a whole chain (fit per expiry over a DataFrame), use the _smile_enrich driver rather than calling fit per slice by hand.