FA-61738 / Options payoff and settlement / Member archive
Implied volatility by bisection with arbitrage bounds: the lower bound uses the undiscounted intrinsic value · case 03
Prices between discounted and undiscounted intrinsic are rejected or solved inconsistently.
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 fixtureThis sample comes from the broken implementation of a controlled reproducer.
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression lower arbitrage bound 1 | 0.0 | null | Failed |
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