""" v1.0 本程序只適用于無股息股票上歐式看漲看跌期權定價 """import matplotlib.pyplot as plt import time from math import exp, sqrt, factorial, log from scipy.stats import norm import multiprocessing as mp from functools import partial# 二叉樹定價函數 def binary_tree(n, S0, K, T, r, sigma, type):"""n: 二叉樹步數S0: 股票價格K: 執行價格T: 期權期限r: 無風險利率sigma: 波動率type: call or put"""dt = T / nu = exp(sigma * sqrt(dt))d = exp(-sigma * sqrt(dt))p = (exp(r * dt) - d) / (u - d)price = 0for j in range(n + 1):price += factorial(n) / (factorial(n - j) * factorial(j)) * pow(p, j) * pow(1 - p, n - j) * max([S0 * u ** j * d ** (n - j) - K, 0])price = price * exp(-r * T)return price# BSM定價函數 def BSM(S0, K, T, r, sigma):d1 = (log(S0 / K) + (r + sigma ** 2 / 2) * T) / (sigma * sqrt(T))d2 = d1 - sigma * sqrt(T)c = S0 * norm.cdf(d1) - K * exp(-r * T) * norm.cdf(d2)p = c + K * exp(-r * T) - S0 # 看跌看漲平價return c, p# 繪圖 def plot(prices, bsm_price):"""prices: 價格序列bsm_price: BSM定價"""n = len(prices)plt.figure()plt.plot(range(1, n + 1), prices, label="binomial tree")plt.plot(range(1, n+1), [bsm_price for i in range(1, n+1)], label="BSM")plt.xlabel("n_step")plt.ylabel("price")plt.legend()plt.show()# 主函數 if __name__ == "__main__":# 參數設置params = {"S0": 50,"K": 52,"T": 2,"r": 0.05,"sigma": 0.3}n = 1000 # 二叉樹步長t0 = time.time() # 開始計時# 并行計算num_cores = int(mp.cpu_count())print("本地計算機有: " + str(num_cores) + " 核心")pool = mp.Pool(num_cores) # 并行計算池par = partial(binary_tree, **params, type="call") # 構造偏函數，方便進行并行計算prices = list(pool.imap(par, range(1, n + 1)))# 運行時間print("共用時%.2f秒" % (time.time() - t0))# BSM定價bsm_price = BSM(**params)[0]# 繪圖plot(prices, bsm_price) """ v2.0 本程序適用于無股息股票上的歐式美式看漲看跌期權定價 由于BSM只適用于不提前行權的期權定價，因此這里不進行BSM定價 """import matplotlib.pyplot as plt import time from math import exp, sqrt from scipy.stats import norm import multiprocessing as mp from functools import partial# 二叉樹定價函數 def binary_tree(n, S0, K, T, r, sigma, is_Euro, is_call):"""n: 二叉樹步數S0: 股票價格K: 執行價格T: 期權期限r: 無風險利率sigma: 波動率is_Euro: True or Falseis_call: True or False"""dt = T / nu = exp(sigma * sqrt(dt))d = exp(-sigma * sqrt(dt))p = (exp(r * dt) - d) / (u - d)# 用二維數組存儲各步股票價格stock_price = []for i in range(n + 1):lst = []for j in range(i + 1):element = S0 * u ** (i - j) * d ** jlst.append(element)stock_price.append(lst)# 分情況計算if is_call: # 計算看漲，此時歐式與美式相同price_last = [max([0, each - K]) for each in stock_price[n]] # 葉子節點的價格for i in range(n):price = []for j in range(n - i):price.append(p * price_last[j] + (1 - p) * price_last[j + 1])price_last = priceelse:price_last = [max([0, K - each]) for each in stock_price[n]]if is_Euro: # 歐式看跌for i in range(n):price = []for j in range(n - i):price.append(p * price_last[j] + (1 - p) * price_last[j + 1])price_last = priceelse: # 美式看跌for i in range(n):price = []for j in range(n - i):p1 = p * price_last[j] + (1 - p) * price_last[j + 1]value = max([p1, K - stock_price[n-i][j]])price.append(value)price_last = pricereturn price[0]# 繪圖 def plot(prices):"""prices: 價格序列"""n = len(prices)plt.figure()plt.plot(range(1, n + 1), prices)plt.xlabel("n_step")plt.ylabel("price")plt.show()# 主程序 if __name__ == "__main__":# 參數設置params = {"S0": 50,"K": 52,"T": 2,"r": 0.05,"sigma": 0.3,"is_Euro": True,"is_call": False}n = 1000 # 二叉樹步長t0 = time.time() # 開始計時# 并行計算num_cores = int(mp.cpu_count())print("本地計算機有: " + str(num_cores) + " 核心")pool = mp.Pool(num_cores) # 并行計算池par = partial(binary_tree, **params) # 構造偏函數，方便進行并行計算prices = list(pool.imap(par, range(1, n + 1)))# 運行時間print("共用時%.2f秒" % (time.time() - t0))# 繪圖plot(prices)

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