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In [1]:

    
import pandas as pd



In [4]:

    
data = pd.read_csv('./vix.csv', index_col='Dates', parse_dates=True)
# statistics
data.describe()









    Out[4]:







  
    
      
      PX_LAST
      PX_OPEN
      PX_HIGH
      PX_LOW
    
  
  
    
      count
      4749.000000
      4749.000000
      4749.000000
      4749.000000
    
    
      mean
      19.682971
      19.805511
      20.599023
      18.991009
    
    
      std
      8.632815
      8.690522
      9.162908
      8.188976
    
    
      min
      9.140000
      9.010000
      9.310000
      8.560000
    
    
      25%
      13.490000
      13.580000
      14.160000
      13.060000
    
    
      50%
      17.550000
      17.640000
      18.250000
      16.830000
    
    
      75%
      23.310000
      23.390000
      24.300000
      22.480000
    
    
      max
      80.860000
      80.740000
      89.530000
      72.760000



In [3]:

    
pct = data.pct_change()  # pct_change
pct.describe()









    Out[3]:







  
    
      
      PX_LAST
      PX_OPEN
      PX_HIGH
      PX_LOW
    
  
  
    
      count
      4748.000000
      4748.000000
      4748.000000
      4748.000000
    
    
      mean
      0.002371
      0.002234
      0.002342
      0.001542
    
    
      std
      0.071894
      0.068930
      0.071511
      0.056878
    
    
      min
      -0.295726
      -0.323188
      -0.370974
      -0.292936
    
    
      25%
      -0.037660
      -0.038124
      -0.036208
      -0.031629
    
    
      50%
      -0.004805
      -0.002590
      -0.003150
      -0.003033
    
    
      75%
      0.033313
      0.034847
      0.032967
      0.030953
    
    
      max
      1.155979
      1.023861
      1.172452
      0.347596



In [4]:

    
largeMove = pct.PX_LAST[pct.PX_LAST > 0.2]
largeMove.describe()
print('-- Prob of larger than 20% move in a day: ', len(largeMove)/len(pct))









    



-- Prob of larger than 20% move in a day:  0.015371657190987577



In [5]:

    
# n-day return
n = 10
ret = data.resample('10D').last()
pct_n = ret.pct_change()
largeMoveN = pct_n.PX_LAST[pct_n.PX_LAST > 0.2]
pct_n.describe()



In [6]:

    
print('-- Prob of larger than 20% move in day: ', n, len(largeMoveN)/len(pct))









    



-- Prob of larger than 20% move in day:  10 0.02695304274584123



In [7]:

    
def count_distance(lst: [float]) -> [(int, int)]:
    """"""



In [13]:

    
def prob(data, window: int, spot: float, strike: float) -> float:
    """
    """
window = 3
data['pct'] = data.PX_LAST.pct_change(periods=window)









    



            PX_LAST  PX_OPEN  PX_HIGH  PX_LOW       pct
Dates                                                  
2000-03-01    24.21    24.36    26.15   23.98       NaN
2000-04-01    27.01    24.94    27.18   24.80       NaN
2000-05-01    26.41    27.98    29.00   25.85       NaN
2000-06-01    25.73    26.68    26.71   24.70  0.062784
2000-07-01    21.72    25.14    25.17   21.72 -0.195853
2000-10-01    21.71    21.89    22.49   21.36 -0.177963
2000-11-01    22.50    21.98    22.63   21.69 -0.125534
2000-12-01    22.84    23.05    23.49   22.41  0.051565
2000-01-13    21.71    22.73    23.10   21.32  0.000000
2000-01-14    19.66    19.83    20.15   19.51 -0.126222
2000-01-18    21.50    21.39    21.63   20.97 -0.058669
2000-01-19    21.72    22.15    22.16   21.44  0.000461
2000-01-20    21.75    21.31    22.60   21.18  0.106307
2000-01-21    20.82    21.55    21.91   20.50 -0.031628
2000-01-24    24.07    21.43    24.44   21.43  0.108195
2000-01-25    23.02    23.79    24.28   22.87  0.058391
2000-01-26    23.03    22.91    23.19   22.45  0.106148
2000-01-27    23.54    22.37    24.39   22.03 -0.022019
2000-01-28    26.14    23.75    26.54   23.17  0.135534
2000-01-31    24.95    26.78    27.43   24.94  0.083370
2000-01-02    23.45    24.43    24.74   23.29 -0.003823
2000-02-02    23.12    23.02    24.74   22.62 -0.115532
2000-03-02    22.01    22.72    23.73   21.93 -0.117836
2000-04-02    21.54    20.77    21.77   20.69 -0.081450
2000-07-02    22.79    22.97    23.27   22.79 -0.014273
2000-08-02    21.25    21.68    22.08   21.17 -0.034530
2000-09-02    22.90    21.54    22.90   21.29  0.063138
2000-10-02    23.07    23.36    23.55   22.75  0.012286
2000-11-02    24.42    22.94    24.80   22.82  0.149176
2000-02-14    24.38    24.67    24.89   24.27  0.064629
...             ...      ...      ...     ...       ...
2018-04-10    14.22    12.84    15.84   12.42  0.185000
2018-05-10    14.82    14.29    17.36   11.72  0.229876
2018-08-10    15.69    16.05    18.38   15.69  0.351421
2018-09-10    15.95    16.12    17.49   15.27  0.121660
2018-10-10    22.96    16.03    22.96   15.83  0.549258
2018-11-10    24.98    23.07    28.84   20.65  0.592097
2018-12-10    21.31    21.63    26.80   20.88  0.336050
2018-10-15    21.30    21.97    22.89   19.47 -0.072300
2018-10-16    17.62    20.28    20.56   17.55 -0.294636
2018-10-17    17.40    17.06    19.55   17.06 -0.183482
2018-10-18    20.06    18.02    21.57   17.51 -0.058216
2018-10-19    19.89    19.24    21.08   18.39  0.128831
2018-10-22    19.64    19.38    20.89   18.82  0.128736
2018-10-23    20.71    22.18    24.66   20.18  0.032403
2018-10-24    25.23    21.60    26.38   20.40  0.268477
2018-10-25    24.22    24.78    24.78   22.06  0.233198
2018-10-26    24.16    24.51    27.52   23.33  0.166586
2018-10-29    24.70    24.48    27.86   22.01 -0.021007
2018-10-30    23.35    23.94    25.55   23.11 -0.035921
2018-10-31    21.23    22.72    22.80   20.39 -0.121275
2018-01-11    19.34    20.96    21.21   19.03 -0.217004
2018-02-11    19.51    18.52    21.61   18.05 -0.164454
2018-05-11    19.96    20.58    20.87   19.64 -0.059821
2018-06-11    19.91    19.84    20.60   19.69  0.029473
2018-07-11    16.36    18.03    18.05   16.33 -0.161456
2018-08-11    16.72    16.18    17.20   16.09 -0.162325
2018-09-11    17.36    16.87    18.41   16.84 -0.128076
2018-12-11    20.45    17.26    20.71   17.25  0.250000
2018-11-13    20.02    19.45    21.25   19.11  0.197368
2018-11-14    19.56    20.52    21.28   19.30  0.126728

[4749 rows x 5 columns]



In [ ]:

	PX_LAST	PX_OPEN	PX_HIGH	PX_LOW
count	691.000000	691.000000	691.000000	691.000000
mean	0.036484	0.034457	0.039159	0.030848
std	0.299564	0.286467	0.309484	0.271347
min	-0.703526	-0.660324	-0.736513	-0.665929
25%	-0.126518	-0.124740	-0.131844	-0.112163
50%	-0.008183	-0.009434	-0.009363	-0.006209
75%	0.134772	0.141477	0.143695	0.126349
max	2.150591	1.718194	1.991817	1.637969

	PX_LAST	PX_OPEN	PX_HIGH	PX_LOW
count	4749.000000	4749.000000	4749.000000	4749.000000
mean	19.682971	19.805511	20.599023	18.991009
std	8.632815	8.690522	9.162908	8.188976
min	9.140000	9.010000	9.310000	8.560000
25%	13.490000	13.580000	14.160000	13.060000
50%	17.550000	17.640000	18.250000	16.830000
75%	23.310000	23.390000	24.300000	22.480000
max	80.860000	80.740000	89.530000	72.760000

	PX_LAST	PX_OPEN	PX_HIGH	PX_LOW
count	4748.000000	4748.000000	4748.000000	4748.000000
mean	0.002371	0.002234	0.002342	0.001542
std	0.071894	0.068930	0.071511	0.056878
min	-0.295726	-0.323188	-0.370974	-0.292936
25%	-0.037660	-0.038124	-0.036208	-0.031629
50%	-0.004805	-0.002590	-0.003150	-0.003033
75%	0.033313	0.034847	0.032967	0.030953
max	1.155979	1.023861	1.172452	0.347596