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+FROM python:3.8.9
+
+WORKDIR /app
+
+COPY ./requirements.txt /app/requirements.txt
+COPY ./packages.txt /app/packages.txt
+
+RUN apt-get update && xargs -r -a /app/packages.txt apt-get install -y && rm -rf /var/lib/apt/lists/*
+RUN pip3 install --no-cache-dir -r /app/requirements.txt
+
+# User
+RUN useradd -m -u 1000 user
+USER user
+ENV HOME /home/user
+ENV PATH $HOME/.local/bin:$PATH
+
+WORKDIR $HOME
+RUN mkdir app
+WORKDIR $HOME/app
+COPY . $HOME/app
+
+EXPOSE 8501
+CMD streamlit run app.py \
+    --server.headless true \
+    --server.enableCORS false \
+    --server.enableXsrfProtection false \
+    --server.fileWatcherType none

app.py

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+import numpy as np
+from scipy.stats import qmc, norm
+import plotly.graph_objects as go
+import streamlit as st
+
+# 設置 Streamlit 頁面的基本配置
+st.set_page_config(page_title="European option",        # 設定網頁標題
+                   layout="wide",                       # 設定頁面布局為寬屏模式
+                   initial_sidebar_state="expanded")    # 初始時側邊欄狀態為展開
+
+st.title("Geometric Brownian motion 模型下，利用模擬方法得到歐式選擇權 (European option) 評價")
+
+with st.sidebar.form(key="my_form"):
+    option_type = st.radio("選擇權型態",
+                           ("Call", "Put"),
+                           horizontal=True)
+
+    S0 = st.slider("選擇期初股價 S0",
+                   min_value=50,
+                   max_value=300,
+                   value=100)
+
+    K = st.slider("選擇履約價格 K",
+                  min_value=50,
+                  max_value=300,
+                  value=100)
+
+    T = st.slider("選擇到期時間 T (年)",
+                  min_value=0.1,
+                  max_value=2.0,
+                  value=1.0,
+                  step=0.1)
+
+    r = st.slider("選擇無風險利率 r",
+                  min_value=0.01,
+                  max_value=0.10,
+                  value=0.03,
+                  step=0.01)
+
+    sigma = st.slider("選擇波動率 σ",
+                      min_value=0.1,
+                      max_value=0.5,
+                      value=0.2,
+                      step=0.05)
+
+    n_simulations = st.slider("選擇模擬次數",
+                              min_value=1000,
+                              max_value=20000,
+                              value=10000,
+                              step=1000)
+
+    n_experiments = st.slider("選擇實驗重複次數",
+                              min_value=100,
+                              max_value=10000,
+                              value=1000,
+                              step=100)
+
+    seed = st.text_input(label="亂數種子", value="123457")
+
+    submit_button = st.form_submit_button(label="Submit")
+
+
+#%%
+# 計算歐式選擇權價格並進行折現
+def European_option_price(S0, K, r, T, sigma, option_type="Call"):
+    # Black-Scholes 公式
+    d1 = (np.log(S0/K)+(r+0.5*sigma**2)*T)/(sigma*np.sqrt(T))
+    d2 = d1-sigma*np.sqrt(T)
+
+    # 真實的 call option 價格
+    if option_type == "Call":
+        true_option_price = S0*norm.cdf(d1)-K*np.exp(-r*T)*norm.cdf(d2)
+
+    # 真實的 put option 價格
+    if option_type == "Put":
+        true_option_price = K*np.exp(-r*T)*norm.cdf(-d2)-S0*norm.cdf(-d1)
+    return true_option_price
+
+def European_option_price_simulation(S0, K, r, T, sigma, z, option_type="Call"):
+    ST = S0*np.exp((r-0.5*sigma**2)*T+sigma*np.sqrt(T)*z)
+    if option_type == "Call":
+        payoff = np.maximum(ST-K, 0)
+    if option_type == "Put":
+        payoff = np.maximum(K-ST, 0)
+    option_price = np.exp(-r*T)*np.mean(payoff)
+    return option_price
+
+option_prices_pseudo, option_prices_quasi, option_prices_numpy = [], [], []
+if submit_button:
+    bar = st.progress(20, "Start calculation")
+    # 顯示進度條
+
+    np.random.seed(int(seed))
+    sobol_engine = qmc.Sobol(d=1, scramble=True, seed=int(seed))
+    for _ in range(n_experiments):
+        # 使用 pseudo-random numbers
+        u_pseudo_uniform = np.random.uniform(0, 1, n_simulations)
+        z_pseudo_random = norm.ppf(u_pseudo_uniform)
+        option_price_pseudo = European_option_price_simulation(S0, K, r, T, sigma, z_pseudo_random, option_type=option_type)
+        option_prices_pseudo.append(option_price_pseudo)
+
+        # 使用 quasi-random numbers
+        u_quasi_random = sobol_engine.random(n=n_simulations).flatten()
+        z_quasi_random = norm.ppf(u_quasi_random)
+        option_price_quasi = European_option_price_simulation(S0, K, r, T, sigma, z_quasi_random, option_type=option_type)
+        option_prices_quasi.append(option_price_quasi)
+
+        # 使用 Numpy random
+        z_numpy_random = np.random.normal(0, 1, n_simulations)
+        option_price_numpy = European_option_price_simulation(S0, K, r, T, sigma, z_numpy_random, option_type=option_type)
+        option_prices_numpy.append(option_price_numpy)
+
+    true_option_price = European_option_price(S0, K, r, T, sigma, option_type=option_type)
+
+    bar = bar.progress(80, "計算中")
+
+
+#%%
+    from plotly.subplots import make_subplots
+
+    st.subheader(option_type+" option 價格分布比較")
+
+    # 創建包含三個子圖的圖表
+    fig = make_subplots(rows=3, cols=1, subplot_titles=("pseudo-random numbers (np.random.uniform)",
+                                                        "quasi-random numbers (qmc.Sobol)",
+                                                        "pseudo-random numbers (np.random.normal)"))
+
+    nbinsx = 30
+    fig.add_trace(
+        go.Histogram(x=option_prices_pseudo,
+                     nbinsx=nbinsx,
+                     histnorm="probability density",
+                     name="pseudo-random numbers (np.random.uniform)",
+                     marker=dict(color="rgba(0,0,255,0.15)", line=dict(width=1, color="black")),
+                     opacity=1.0),
+        row=1, col=1)
+
+    fig.add_trace(
+        go.Histogram(x=option_prices_quasi,
+                     nbinsx=nbinsx,
+                     histnorm="probability density",
+                     name="quasi-random numbers (qmc.Sobol)",
+                     marker=dict(color="rgba(255,0,0,0.15)", line=dict(width=1, color="black")),
+                     opacity=1.0),
+        row=2, col=1)
+
+    fig.add_trace(
+        go.Histogram(x=option_prices_numpy,
+                     nbinsx=nbinsx,
+                     histnorm="probability density",
+                     name="pseudo-random numbers (np.random.normal)",
+                     marker=dict(color="rgba(0,255,0,0.15)", line=dict(width=1, color="black")),
+                     opacity=1.0),
+        row=3, col=1)
+
+    fig.add_vline(x=true_option_price,
+                  line_width=2,
+                  line_dash="dash",
+                  line_color="blue")
+
+    fig.update_layout(
+        title="不同方法計算的 "+option_type+" option 價格分布",
+        height=900)
+
+    fig.update_xaxes(title=option_type+" option 價格", row=1, col=1)
+    fig.update_xaxes(title=option_type+" option 價格", row=2, col=1)
+    fig.update_xaxes(title=option_type+" option 價格", row=3, col=1)
+
+    fig.update_yaxes(title="density", row=1, col=1)
+    fig.update_yaxes(title="density", row=2, col=1)
+    fig.update_yaxes(title="density", row=3, col=1)
+
+    st.plotly_chart(fig)
+
+    bar = bar.progress(100, "OK")
+
+# 打開 "命令提示字元" 或 "終端機"，開始執行程式 (或進入 Command Prompt 視窗)：
+# (a) Anaconda => Anaconda Prompt (or Anaconda Powershell Prompt)
+# (b) WinPython => WinPython Command Prompt.exe
+# Streamlit run "c:\work\subject\112\simulation\tronclass\(2024.03.21) pseudo-random numbers vs quasi-random numbers-european_option\03-pseudo-random numbers vs quasi-random numbers-european_option-streamlit2.py"
+# Google Chrome => http://localhost:8501/
+# Google Chrome 不關掉，程式修改存檔後，可直接執行 Google Chrome output 畫面右上角的 Return。
+# 指定 localhost port => streamlit run app.py --server.port 8502
+# 需要終止該應用程式只需在終端中按 Ctrl + C。
+# 路徑和檔名不能有中文。
+# Mac 不能使用 MacOS 內建的 Safari 瀏覽器，改用 Google Chrome 就沒問題了。