monte_carlo.py

import numpy as np
import matplotlib.pyplot as plt
import streamlit as st

def monte_carlo_option_price(
    S, K, T, r, sigma, simulations=100_000, steps=1,
    option_type="call", asian=False, confidence_level=0.95
):
    np.random.seed(42)
    dt = T / steps
    Z = np.random.standard_normal((simulations, steps))
    price_paths = np.zeros((simulations, steps + 1))
    price_paths[:, 0] = S

    for t in range(1, steps + 1):
        price_paths[:, t] = price_paths[:, t - 1] * np.exp(
            (r - 0.5 * sigma**2) * dt + sigma * np.sqrt(dt) * Z[:, t - 1]
        )

    if asian:
        avg_price = price_paths[:, 1:].mean(axis=1)
        payoff = np.maximum(avg_price - K, 0) if option_type == "call" else np.maximum(K - avg_price, 0)
    else:
        ST = price_paths[:, -1]
        payoff = np.maximum(ST - K, 0) if option_type == "call" else np.maximum(K - ST, 0)

    discounted = np.exp(-r * T) * payoff
    mean_price = discounted.mean()
    std_err = discounted.std(ddof=1) / np.sqrt(simulations)

    z_score = 1.96
    ci = (mean_price - z_score * std_err, mean_price + z_score * std_err)

    return mean_price, ci


def plot_price_paths(S, T, r, sigma, simulations=10, steps=50, barrier=None, highlight_barrier=False):
    """
    Simulate and plot GBM price paths.
    
    If highlight_barrier=True, show breached paths in red, safe paths in green.
    """
    np.random.seed(1)
    dt = T / steps
    Z = np.random.standard_normal((simulations, steps))
    paths = np.zeros((simulations, steps + 1))
    paths[:, 0] = S

    for t in range(1, steps + 1):
        paths[:, t] = paths[:, t - 1] * np.exp(
            (r - 0.5 * sigma ** 2) * dt + sigma * np.sqrt(dt) * Z[:, t - 1]
        )

    fig, ax = plt.subplots(figsize=(10, 6))

    for i in range(simulations):
        path = paths[i]
        if highlight_barrier and barrier is not None:
            if (path >= barrier).any():
                ax.plot(path, color="red", lw=1)  # 🔴 Breached
            else:
                ax.plot(path, color="green", lw=1)  # 🟢 Safe
        else:
            ax.plot(path, lw=1)

    ax.set_title("Simulated GBM Price Paths")
    ax.set_xlabel("Time Steps")
    ax.set_ylabel("Stock Price")
    ax.grid(True)

    if barrier is not None:
        ax.axhline(barrier, color="orange", linestyle="--", label="Barrier")
        ax.legend()

    st.pyplot(fig)