克隆策略
In [15]:
import math
import numpy as np
import time
import pandas as pd

# np.random.seed(20000) 
t_0 = time.time()
# 参数
def data_fetcher():
    data_info = DataSource('basic_info_CN_OPTION').read(start_date='2019-01-01')
    df_hq = DataSource('bar1d_CN_OPTION').read(start_date='2019-01-01')
    df_merge = data_info.merge(df_hq,on=['instrument'])
    df_merge['days_todelist'] = ((df_merge['delist_date'] - df_merge['date'])/np.timedelta64(1, 'D')).astype(int)
    df_option = df_merge[['date','instrument','settle', 'strike_direction','strike_price','days_todelist']]
    df_option['settle'] = df_merge[['close']]
    return df_option
In [16]:
def volatility():
    df_option = data_fetcher()
    df_index = DataSource('bar1d_CN_FUND').read(instruments=['510050.HOF'],start_date='2019-02-27', end_date='2019-09-26')[['date', 'close']]
    df_index['std_year'] = 252**0.5*np.std(np.log(df_index['close']/df_index['close'].shift(1)))
    df_index['std_daily'] = np.std(np.log(df_index['close']/df_index['close'].shift(1)))
    df_final = df_index.merge(df_option,on='date')
    return df_final
In [17]:
def call_option_price():
    option_data = volatility()
    option_data = option_data[option_data['instrument'] == '10001749.SHAO']
    sigma = option_data['std_year'].mean()#波动率
    risk_free_rate = 0.03#无风险利率
    time_to_maturity = np.array(option_data['days_todelist'])#计算出的到期天数
    divide = 50 #到期天数对应的时间区间数
    time_interval = time_to_maturity/divide#每个区间长度
    N = 50000#随机变量模拟数量
    exercise_prise = np.array(option_data['strike_price'])#行权价
    gauss = np.random.standard_normal((len(time_to_maturity), divide + 1, N))#生成三维高斯随机变量
    time_interval = time_to_maturity/divide#每个区间长度
    fund_prise_0 = option_data.settle.values[0]
    fund_prise_log = np.log(fund_prise_0) + np.array([np.cumsum((risk_free_rate - 0.5 * sigma ** 2) * time_interval[i] + sigma * np.sqrt(time_interval[i]) * gauss[i], axis=0) for i in range(0, len(time_to_maturity))])
    fund_prise = np.exp(fund_prise_log)
    fund_prise[:,0:1,:] = fund_prise_0
    call_option_prise = [np.exp(-risk_free_rate * time_to_maturity[i]) * np.sum(np.maximum(fund_prise[i][-1] - exercise_prise[i], 0)) / N for i in range(0, len(time_to_maturity))]
    errors = call_option_prise - np.array(option_data['settle'])
    errors = pd.Series(errors, index=option_data['date'])
    call_option_prise = pd.Series(call_option_prise, index=option_data['date'])
    return '看涨期权定价为：', call_option_prise, '绝对误差为：', errors, '程序运行时间为：', np.round(time.time() - t_0, 1), 's.'
In [18]:
a = call_option_price()
a
Out[18]:
('看涨期权定价为：', date
 2019-02-27    0.287249
 2019-02-28    0.298701
 2019-03-01    0.379017
 2019-03-04    0.295021
 2019-03-05    0.311811
 2019-03-06    0.286657
 2019-03-07    0.347475
 2019-03-08    0.371281
 2019-03-11    0.364393
 2019-03-12    0.309484
 2019-03-13    0.401991
 2019-03-14    0.415961
 2019-03-15    0.291768
 2019-03-18    0.306029
 2019-03-19    0.296864
 2019-03-20    0.326924
 2019-03-21    0.296761
 2019-03-22    0.324629
 2019-03-25    0.309562
 2019-03-26    0.300076
 2019-03-27    0.281743
 2019-03-28    0.322113
 2019-03-29    0.295321
 2019-04-01    0.294642
 2019-04-02    0.297239
 2019-04-03    0.299548
 2019-04-04    0.320931
 2019-04-08    0.273584
 2019-04-09    0.329734
 2019-04-10    0.275416
                 ...   
 2019-08-14    0.069745
 2019-08-15    0.065249
 2019-08-16    0.059192
 2019-08-19    0.049838
 2019-08-20    0.047450
 2019-08-21    0.045544
 2019-08-22    0.042190
 2019-08-23    0.035907
 2019-08-26    0.028849
 2019-08-27    0.028259
 2019-08-28    0.023743
 2019-08-29    0.021800
 2019-08-30    0.016285
 2019-09-02    0.012405
 2019-09-03    0.008620
 2019-09-04    0.007732
 2019-09-05    0.006864
 2019-09-06    0.004627
 2019-09-09    0.002460
 2019-09-10    0.001449
 2019-09-11    0.000964
 2019-09-12    0.000622
 2019-09-16    0.000042
 2019-09-17    0.000054
 2019-09-18    0.000032
 2019-09-19    0.000000
 2019-09-20    0.000000
 2019-09-23    0.000000
 2019-09-24    0.000000
 2019-09-25    0.000000
 Length: 142, dtype: float64, '绝对误差为：', date
 2019-02-27   -0.004151
 2019-02-28    0.019101
 2019-03-01    0.131717
 2019-03-04    0.051621
 2019-03-05    0.057411
 2019-03-06    0.023057
 2019-03-07    0.056075
 2019-03-08    0.028881
 2019-03-11    0.050093
 2019-03-12   -0.011216
 2019-03-13    0.089291
 2019-03-14    0.100761
 2019-03-15    0.000068
 2019-03-18    0.040429
 2019-03-19    0.017564
 2019-03-20    0.048824
 2019-03-21    0.012961
 2019-03-22    0.042529
 2019-03-25   -0.010338
 2019-03-26   -0.023824
 2019-03-27   -0.017457
 2019-03-28    0.020713
 2019-03-29    0.046421
 2019-04-01    0.063842
 2019-04-02    0.071539
 2019-04-03    0.081548
 2019-04-04    0.111631
 2019-04-08    0.069784
 2019-04-09    0.134734
 2019-04-10    0.077516
                 ...   
 2019-08-14   -0.071255
 2019-08-15   -0.067251
 2019-08-16   -0.071108
 2019-08-19   -0.039862
 2019-08-20   -0.041550
 2019-08-21   -0.038856
 2019-08-22   -0.038910
 2019-08-23   -0.024793
 2019-08-26   -0.057451
 2019-08-27   -0.039741
 2019-08-28   -0.055657
 2019-08-29   -0.062100
 2019-08-30   -0.060015
 2019-09-02   -0.047895
 2019-09-03   -0.051580
 2019-09-04   -0.032268
 2019-09-05   -0.019036
 2019-09-06   -0.012173
 2019-09-09   -0.014340
 2019-09-10   -0.016051
 2019-09-11   -0.016236
 2019-09-12   -0.007378
 2019-09-16   -0.006758
 2019-09-17   -0.013646
 2019-09-18   -0.008768
 2019-09-19   -0.005500
 2019-09-20   -0.003500
 2019-09-23   -0.004300
 2019-09-24   -0.001000
 2019-09-25   -0.000100
 Length: 142, dtype: float64, '程序运行时间为：', 62.6, 's.')