ypchangchatgpt/European_option-streamlit-plotly-docker

1import numpy as np2from scipy.stats import qmc, norm3import plotly.graph_objects as go4import streamlit as st5 6# 設置 Streamlit 頁面的基本配置7st.set_page_config(page_title="European option",        # 設定網頁標題8                   layout="wide",                       # 設定頁面布局為寬屏模式9                   initial_sidebar_state="expanded")    # 初始時側邊欄狀態為展開10 11st.title("Geometric Brownian motion 模型下，利用模擬方法得到歐式選擇權 (European option) 評價")12 13with st.sidebar.form(key="my_form"):14    option_type = st.radio("選擇權型態",15                           ("Call", "Put"),16                           horizontal=True)17 18    S0 = st.slider("選擇期初股價 S0",19                   min_value=50,20                   max_value=300,21                   value=100)22 23    K = st.slider("選擇履約價格 K",24                  min_value=50,25                  max_value=300,26                  value=100)27 28    T = st.slider("選擇到期時間 T (年)",29                  min_value=0.1,30                  max_value=2.0,31                  value=1.0,32                  step=0.1)33 34    r = st.slider("選擇無風險利率 r",35                  min_value=0.01,36                  max_value=0.10,37                  value=0.03,38                  step=0.01)39 40    sigma = st.slider("選擇波動率 σ",41                      min_value=0.1,42                      max_value=0.5,43                      value=0.2,44                      step=0.05)45 46    n_simulations = st.slider("選擇模擬次數",47                              min_value=1000,48                              max_value=20000,49                              value=10000,50                              step=1000)51 52    n_experiments = st.slider("選擇實驗重複次數",53                              min_value=100,54                              max_value=10000,55                              value=1000,56                              step=100)57 58    seed = st.text_input(label="亂數種子", value="123457")59 60    submit_button = st.form_submit_button(label="Submit")61 62 63#%%64# 計算歐式選擇權價格並進行折現65def European_option_price(S0, K, r, T, sigma, option_type="Call"):66    # Black-Scholes 公式67    d1 = (np.log(S0/K)+(r+0.5*sigma**2)*T)/(sigma*np.sqrt(T))68    d2 = d1-sigma*np.sqrt(T)69 70    # 真實的 call option 價格71    if option_type == "Call":72        true_option_price = S0*norm.cdf(d1)-K*np.exp(-r*T)*norm.cdf(d2)73 74    # 真實的 put option 價格75    if option_type == "Put":76        true_option_price = K*np.exp(-r*T)*norm.cdf(-d2)-S0*norm.cdf(-d1)77    return true_option_price78 79def European_option_price_simulation(S0, K, r, T, sigma, z, option_type="Call"):80    ST = S0*np.exp((r-0.5*sigma**2)*T+sigma*np.sqrt(T)*z)81    if option_type == "Call":82        payoff = np.maximum(ST-K, 0)83    if option_type == "Put":84        payoff = np.maximum(K-ST, 0)85    option_price = np.exp(-r*T)*np.mean(payoff)86    return option_price87 88option_prices_pseudo, option_prices_quasi, option_prices_numpy = [], [], []89if submit_button:90    bar = st.progress(20, "Start calculation")91    # 顯示進度條92 93    np.random.seed(int(seed))94    sobol_engine = qmc.Sobol(d=1, scramble=True, seed=int(seed))95    for _ in range(n_experiments):96        # 使用 pseudo-random numbers97        u_pseudo_uniform = np.random.uniform(0, 1, n_simulations)98        z_pseudo_random = norm.ppf(u_pseudo_uniform)99        option_price_pseudo = European_option_price_simulation(S0, K, r, T, sigma, z_pseudo_random, option_type=option_type)100        option_prices_pseudo.append(option_price_pseudo)101 102        # 使用 quasi-random numbers103        u_quasi_random = sobol_engine.random(n=n_simulations).flatten()104        z_quasi_random = norm.ppf(u_quasi_random)105        option_price_quasi = European_option_price_simulation(S0, K, r, T, sigma, z_quasi_random, option_type=option_type)106        option_prices_quasi.append(option_price_quasi)107 108        # 使用 Numpy random109        z_numpy_random = np.random.normal(0, 1, n_simulations)110        option_price_numpy = European_option_price_simulation(S0, K, r, T, sigma, z_numpy_random, option_type=option_type)111        option_prices_numpy.append(option_price_numpy)112 113    true_option_price = European_option_price(S0, K, r, T, sigma, option_type=option_type)114 115    bar = bar.progress(80, "計算中")116 117 118#%%119    from plotly.subplots import make_subplots120 121    st.subheader(option_type+" option 價格分布比較")122 123    # 創建包含三個子圖的圖表124    fig = make_subplots(rows=3, cols=1, subplot_titles=("pseudo-random numbers (np.random.uniform)",125                                                        "quasi-random numbers (qmc.Sobol)",126                                                        "pseudo-random numbers (np.random.normal)"))127 128    nbinsx = 30129    fig.add_trace(130        go.Histogram(x=option_prices_pseudo,131                     nbinsx=nbinsx,132                     histnorm="probability density",133                     name="pseudo-random numbers (np.random.uniform)",134                     marker=dict(color="rgba(0,0,255,0.15)", line=dict(width=1, color="black")),135                     opacity=1.0),136        row=1, col=1)137 138    fig.add_trace(139        go.Histogram(x=option_prices_quasi,140                     nbinsx=nbinsx,141                     histnorm="probability density",142                     name="quasi-random numbers (qmc.Sobol)",143                     marker=dict(color="rgba(255,0,0,0.15)", line=dict(width=1, color="black")),144                     opacity=1.0),145        row=2, col=1)146 147    fig.add_trace(148        go.Histogram(x=option_prices_numpy,149                     nbinsx=nbinsx,150                     histnorm="probability density",151                     name="pseudo-random numbers (np.random.normal)",152                     marker=dict(color="rgba(0,255,0,0.15)", line=dict(width=1, color="black")),153                     opacity=1.0),154        row=3, col=1)155 156    fig.add_vline(x=true_option_price,157                  line_width=2,158                  line_dash="dash",159                  line_color="blue")160 161    fig.update_layout(162        title="不同方法計算的 "+option_type+" option 價格分布",163        height=900)164 165    fig.update_xaxes(title=option_type+" option 價格", row=1, col=1)166    fig.update_xaxes(title=option_type+" option 價格", row=2, col=1)167    fig.update_xaxes(title=option_type+" option 價格", row=3, col=1)168 169    fig.update_yaxes(title="density", row=1, col=1)170    fig.update_yaxes(title="density", row=2, col=1)171    fig.update_yaxes(title="density", row=3, col=1)172 173    st.plotly_chart(fig)174 175    bar = bar.progress(100, "OK")176 177# 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)：178# (a) Anaconda => Anaconda Prompt (or Anaconda Powershell Prompt)179# (b) WinPython => WinPython Command Prompt.exe180# 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"181# Google Chrome => http://localhost:8501/182# 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。183# 指定 localhost port => streamlit run app.py --server.port 8502184# 需要終止該應用程式只需在終端中按 Ctrl + C。185# 路徑和檔名不能有中文。186# Mac 不能使用 MacOS 內建的 Safari 瀏覽器，改用 Google Chrome 就沒問題了。187