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import numpy as np |
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from scipy import stats |
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import matplotlib |
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import matplotlib.pyplot as plt |
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import mpltw |
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matplotlib.use("Agg") |
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font_size = 8 |
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plt.rcParams.update({"font.size": font_size}) |
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plt.close("all") |
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def generate_Sobol(Sobol_seq, n=1, epsilon=0): |
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quasi_random_numbers = Sobol_seq.random(n) |
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d = Sobol_seq.d |
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l_bounds = np.repeat(epsilon, d) |
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u_bounds = np.repeat(1-epsilon, d) |
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quasi_random_numbers = stats.qmc.scale(quasi_random_numbers, l_bounds, u_bounds) |
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return quasi_random_numbers |
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def Black_Scholes(S0, K, r, T, sigma, option_type): |
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d1 = (np.log(S0/K)+(r+sigma**2/2)*T)/(sigma*np.sqrt(T)) |
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d2 = d1-sigma*np.sqrt(T) |
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if option_type == "call": |
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return S0*stats.norm.cdf(d1)-K*np.exp(-r*T)*stats.norm.cdf(d2) |
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if option_type == "put": |
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return K*np.exp(-r*T)*stats.norm.cdf(-d2)-S0*stats.norm.cdf(-d1) |
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def European_option_simulation(S0, K, r, T, sigma, Z): |
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ST = S0*np.exp((r-0.5*sigma**2)*T+sigma*np.sqrt(T)*Z) |
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payoff = np.maximum(ST-K, 0) |
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prices = np.exp(-r*T)*np.mean(payoff, axis=0) |
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return prices |
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def plot_European_option(S0, K, r, T, sigma, n, m, seed, bins, alpha): |
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S0 = np.float64(S0) |
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K = np.float64(K) |
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r = np.float64(r) |
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T = np.float64(T) |
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sigma = np.float64(sigma) |
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price_true = Black_Scholes(S0, K, r, T, sigma, option_type="call") |
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print("European call option price =", price_true) |
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n = int(n) |
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m = int(m) |
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seed = int(seed) |
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bins = int(bins) |
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alpha = np.float64(alpha) |
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np.random.seed(seed) |
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u_pseudo = np.random.rand(n, m) |
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Z_pseudo = stats.norm.ppf(u_pseudo) |
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Sobol_seq = stats.qmc.Sobol(d=m, scramble=True, seed=seed) |
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""" |
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scramble 內建值為 True。 |
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Scramble 是指將一個序列或集合中的元素加干擾的過程。 |
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""" |
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u_quasi = generate_Sobol(Sobol_seq, n=n, epsilon=1e-8) |
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Z_quasi = stats.norm.ppf(u_quasi) |
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""" |
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Sobol_seq = stats.qmc.Sobol(d=n, seed=seed) |
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u_quasi = Sobol_seq.random(m) |
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Z_quasi = stats.norm.ppf(u_quasi).T |
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# 這個寫法沒有明顯效果，所以要注意 d 的設定。 |
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""" |
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prices_pseudo = European_option_simulation(S0, K, r, T, sigma, Z_pseudo) |
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prices_quasi = European_option_simulation(S0, K, r, T, sigma, Z_quasi) |
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fig = plt.figure(figsize=(4, 8)) |
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plt.subplot(211) |
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plt.hist(prices_pseudo, |
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bins=bins, |
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density=True, |
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alpha=alpha, |
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ec="black") |
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plt.axvline(x=price_true, color="red") |
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plt.xlabel("simulate option price") |
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plt.ylabel("density") |
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plt.title("Simulate option prices with pseudo-random numbers") |
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plt.subplot(212) |
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plt.hist(prices_quasi, |
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bins=bins, |
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density=True, |
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alpha=alpha, |
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ec="black") |
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plt.axvline(x=price_true, color="red") |
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plt.xlabel("simulate option price") |
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plt.ylabel("density") |
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plt.title("Simulate option prices with quasi-random numbers") |
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plt.tight_layout() |
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return fig |
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import gradio as gr |
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S0 = gr.Textbox(value="100", label="S0") |
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K = gr.Textbox(value="100", label="K") |
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r = gr.Textbox(value="0.02", label="r") |
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T = gr.Textbox(value="0.5", label="T") |
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sigma = gr.Textbox(value="0.2", label="sigma") |
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n = gr.Textbox(value="10000", label="n") |
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m = gr.Textbox(value="1000", label="m") |
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seed = gr.Textbox(value="123457", label="seed") |
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bins = gr.Slider(minimum=10, maximum=60, step=5, value=40, label="bins") |
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alpha = gr.Slider(minimum=0, maximum=1, step=0.1, value=0.6, label="alpha") |
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inputs = [S0, K, r, T, sigma, n, m, seed, bins, alpha] |
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outputs = [gr.Plot()] |
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interface = gr.Interface(fn=plot_European_option, |
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inputs=inputs, |
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outputs=outputs, |
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title="European call option") |
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interface.launch(share=True) |
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