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# SPDX-License-Identifier: Apache-2.0
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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import numpy as np


def black_scholes_mc(S0, K, r, sigma, T, n_paths, n_steps):
    dt = T / n_steps
    paths = np.zeros((n_paths, n_steps + 1))
    paths[:, 0] = S0
    for t in range(1, n_steps + 1):
        z = np.random.randn(n_paths)
        paths[:, t] = paths[:, t - 1] * np.exp(
            (r - 0.5 * sigma * sigma) * dt + sigma * np.sqrt(dt) * z
        )
    payoff = np.maximum(paths[:, -1] - K, 0.0)
    price = np.exp(-r * T) * np.mean(payoff)
    return price