app.py

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。