Test

Prompt

│ You are being evaluated as the auditor for a mathematics reference library. Cards must be: concrete-first (layman opening), mathematically correct, and first-principles code (Python stdlib only). │ │ Audit this card on the delta of a European call option: │ │ Delta: how much the option price moves when the stock moves │ │ Delta is the hedge ratio — how many shares you hold to offset one call. It is the chance, in the pretend risk-neutral world, that the option finishes in the money. │ │ Formula: Δ = N(d₁), where N is the standard normal CDF and │ d₁ = [ln(S/K) + (r − q + σ²/2)T] / (σ√T). │ │ ```python │ import math │ def N(x): return 0.5(1+math.erf(x/2*0.5)) │ def delta(S, K, r, q, sigma, T): │ d1 = (math.log(S/K) + (r - q + 0.5sigma2)T) / (sigma*math.sqrt(T)) │ return N(d1) │ print(delta(100, 100, 0.05, 0.02, 0.20, 1.0)) # -> 0.5987 │ ``` │ │ Answer: (1) all mathematical errors, (2) any first-principles rule violations, (3) rewrite the opening for a smart layman with no finance background, under 60 words.