# 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)
# 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 可以不寫。