Test
Prompt
β 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). β β Audit this card on the delta of a European call option: β β Delta: how much the option price moves when the stock moves β β Delta is the hedge ratio β 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. β β Formula: Ξ = N(dβ), where N is the standard normal CDF and β dβ = [ln(S/K) + (r β q + ΟΒ²/2)T] / (ΟβT). β β ```python β import math β def N(x): return 0.5(1+math.erf(x/2*0.5)) β def delta(S, K, r, q, sigma, T): β d1 = (math.log(S/K) + (r - q + 0.5sigma2)T) / (sigma*math.sqrt(T)) β return N(d1) β print(delta(100, 100, 0.05, 0.02, 0.20, 1.0)) # -> 0.5987 β ``` β β 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.
