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app.py

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+# 不使用 for 迴圈。
+# 發佈到 Hugging Face 伺服器，程式不能有 %reset -f (magic functions)
+
+import numpy as np
+from scipy import stats
+import matplotlib
+import matplotlib.pyplot as plt
+import mpltw
+
+matplotlib.use("Agg")
+# 使用 gradio+matplotlib 套件，這行一定要寫。
+
+font_size = 8
+plt.rcParams.update({"font.size": font_size})
+
+plt.close("all")
+
+
+#%%
+# quasi-random numbers 時，調整避免產生的模擬資料是 0 或 1。
+# 寫為函數：
+def generate_Sobol(Sobol_seq, n=1, epsilon=0):
+    quasi_random_numbers = Sobol_seq.random(n)
+    # quasi_random_numbers = epsilon + (1 - 2 * epsilon) * quasi_random_numbers
+    d = Sobol_seq.d
+    l_bounds = np.repeat(epsilon, d)
+    u_bounds = np.repeat(1-epsilon, d)
+    quasi_random_numbers = stats.qmc.scale(quasi_random_numbers, l_bounds, u_bounds)
+    return quasi_random_numbers
+
+def Black_Scholes(S0, K, r, T, sigma, option_type):
+    d1 = (np.log(S0/K)+(r+sigma**2/2)*T)/(sigma*np.sqrt(T))
+    d2 = d1-sigma*np.sqrt(T)
+    if option_type == "call":
+        return S0*stats.norm.cdf(d1)-K*np.exp(-r*T)*stats.norm.cdf(d2)
+    if option_type == "put":
+        return K*np.exp(-r*T)*stats.norm.cdf(-d2)-S0*stats.norm.cdf(-d1)
+
+def European_option_simulation(S0, K, r, T, sigma, Z):
+    ST = S0*np.exp((r-0.5*sigma**2)*T+sigma*np.sqrt(T)*Z)
+    payoff = np.maximum(ST-K, 0)
+    prices = np.exp(-r*T)*np.mean(payoff, axis=0)
+    return prices
+
+
+#%%
+def plot_European_option(S0, K, r, T, sigma, n, m, seed, bins, alpha):
+    S0 = np.float64(S0)
+    K = np.float64(K)
+    r = np.float64(r)
+    T = np.float64(T)
+    sigma = np.float64(sigma)
+
+    price_true = Black_Scholes(S0, K, r, T, sigma, option_type="call")
+    print("European call option price =", price_true)
+
+    n = int(n)
+    m = int(m)
+    seed = int(seed)
+    bins = int(bins)
+    alpha = np.float64(alpha)
+
+    # pseudo-random numbers
+    np.random.seed(seed)
+    u_pseudo = np.random.rand(n, m)
+    Z_pseudo = stats.norm.ppf(u_pseudo)
+
+    # quasi-random numbers
+    Sobol_seq = stats.qmc.Sobol(d=m, scramble=True, seed=seed)
+    """
+    scramble 內建值為 True。
+    Scramble 是指將一個序列或集合中的元素加干擾的過程。
+    """
+
+    u_quasi = generate_Sobol(Sobol_seq, n=n, epsilon=1e-8)
+    Z_quasi = stats.norm.ppf(u_quasi)
+    """
+    Sobol_seq = stats.qmc.Sobol(d=n, seed=seed)
+    u_quasi = Sobol_seq.random(m)
+    Z_quasi = stats.norm.ppf(u_quasi).T
+    # 這個寫法沒有明顯效果，所以要注意 d 的設定。
+    """
+
+    prices_pseudo = European_option_simulation(S0, K, r, T, sigma, Z_pseudo)
+    prices_quasi = European_option_simulation(S0, K, r, T, sigma, Z_quasi)
+
+    fig = plt.figure(figsize=(4, 8))
+    plt.subplot(211)
+    plt.hist(prices_pseudo,
+             bins=bins,
+             density=True,
+             alpha=alpha,
+             ec="black")
+    plt.axvline(x=price_true, color="red")
+    plt.xlabel("simulate option price")
+    plt.ylabel("density")
+    plt.title("Simulate option prices with pseudo-random numbers")
+
+    plt.subplot(212)
+    plt.hist(prices_quasi,
+             bins=bins,
+             density=True,
+             alpha=alpha,
+             ec="black")
+    plt.axvline(x=price_true, color="red")
+    plt.xlabel("simulate option price")
+    plt.ylabel("density")
+    plt.title("Simulate option prices with quasi-random numbers")
+
+    plt.tight_layout()
+    return fig
+
+
+#%%
+import gradio as gr
+
+S0 = gr.Textbox(value="100", label="S0")        # initial stock price
+K = gr.Textbox(value="100", label="K")          # strike price
+r = gr.Textbox(value="0.02", label="r")         # risk-free interest rate
+T = gr.Textbox(value="0.5", label="T")          # time to maturity
+sigma = gr.Textbox(value="0.2", label="sigma")  # volatility
+n = gr.Textbox(value="10000", label="n")        # number of simulations
+m = gr.Textbox(value="1000", label="m")         # number of repeated experiments
+seed = gr.Textbox(value="123457", label="seed")
+bins = gr.Slider(minimum=10, maximum=60, step=5, value=40, label="bins")
+alpha = gr.Slider(minimum=0, maximum=1, step=0.1, value=0.6, label="alpha")
+inputs = [S0, K, r, T, sigma, n, m, seed, bins, alpha]
+
+outputs = [gr.Plot()]
+
+interface = gr.Interface(fn=plot_European_option,
+                         inputs=inputs,
+                         outputs=outputs,
+                         title="European call option")
+
+interface.launch()
+# share=True 一定要寫，瀏覽器才可以看到結果。
+# 但發佈到 Hugging Face 伺服器，則 share=True 不能寫。

requirements.txt

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+numpy
+scipy 
+matplotlib
+mpltw
+gradio