Black-Scholes European Call Pricing

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Problem

Implement a function to calculate the Black-Scholes price of a European call option.

Use continuous compounding and the standard normal cumulative distribution function. Return the option price as a floating-point number.

Signature: def black_scholes_call(S, K, T, r, sigma):

Inputs are spot price S, strike price K, time to expiration T in years, continuously compounded risk-free rate r, and volatility sigma. Define the price at T = 0 as max(S - K, 0), and handle sigma = 0 using its deterministic limit.

Constraints

0 < S
0 < K
0 <= T
r may be positive, zero, or negative
0 <= sigma
Use floating-point arithmetic
Answers are judged with a tolerance of 1e-9

Function Signature

def black_scholes_call(S, K, T, r, sigma):

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