Module implied_vol 

Implied volatility

Invert a European market premium → annualized σ for BSM, Black ’76, or Garman–Kohlhagen (same Newton + bisection core).

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Trading perspective

The market does not quote “model vol”; it quotes prices. IV is the σ that makes the model match that price — the language of surfaces, skew, and “IV crush”.

Use	How
Mark a book	Mid → IV → store on the contract
Relative value	Compare IV across strikes/expiries (skew, term structure)
Events	IV vs realized (realized from underlier returns / TA path)

Gotchas desks already know: American early exercise, discrete dividends, and wide markets break naive European IV — treat results as model-dependent.

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Engineering perspective

• Solver: Newton–Raphson on vega, Brent bracketed fallback (not plain bisection).
• Model vol field is ignored as a seed (only other market/contract inputs matter).
• Prefer *State::set_vol_from_price in live loops so IV is stored once.
• Hot path cost: a handful of model evaluations — fine per quote; batch chains may parallelize across strikes in your engine.

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Word problem

Market call mid is ~10.45 with S=K=100, T=1, r=5%, q=0. What is IV?

Expect: about 20%.

use finance_solution::derivatives::{
    bsm_implied_vol, BsmParams, OptionType,
};
let p = BsmParams::atm_one_year(100.0, 0.05, 0.20);
let iv = bsm_implied_vol(p, OptionType::Call, 10.4506).unwrap();
assert!((iv - 0.20).abs() < 1e-3);

Functions

bsm_implied_vol

Solve for annualized vol given a target BSM premium.