FA-61750 / Options payoff and settlement / Member archive

Implied volatility by bisection with arbitrage bounds: prices at or above the upper bound are solved · case 05

Arbitrage-violating prices return the bracket edge instead of None.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Inputs kind, option price, S, K, r, T (no dividends). If price <= lower bound (call max(S - K e^{-rT},0), put max(K e^{-rT} - S,0)) or price >= upper bound (call S, put K e^{-rT}) return None. Otherwise bisect sigma in [1e-6, 5] for 100 iterations on the Black-Scholes price and return the midpoint rounded to 4.

Why this case matters

Option expiry, exercise and settlement engines move cash and shares; a wrong branch misstates obligations.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression upper arbitrage bound 1	`5.0`	`null`	Failed

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