Historical volatility

Is 20% a lot? Paste a price history, or generate one, and measure the volatility the market actually delivered. Compare it with the implied volatility the option pages have been solving for, watch it move through time, and see whether real returns look like the normal distribution Black-Scholes assumes.

Prices

00
86
81
49
67
01
92
67
66
20
86
45
79
39
57
36
00
34
97
53
37
38
89
12
91
62
33
93
06
71
52
24
16
96
45
98
43
02
22
42
72
87
72
92
63
25
70
50
91
91
60
41
72
28
60
05
88
82
91
00
95
25
85
88
59
65
43
54
49
42
52
61
40
93
50
51
68
90
93
96
65
78
20
54
85
27
07
22
41
75
89
20
42
18
28
56
93
82
33
70
76
65
02
36
11
58
29
27
82
16
83
51
35
14
15
38
44
46
28
58
20
76
34
11
07
61
04
91
22
44
65
39
26
80
24
76
48
02
76
09
84
61
56
56
38
59
73
51
22
66
73
87
90
27
07
21
64
51
39
24
38
64
81
56
26
11
91
98
52
86
92
91
57
94
51
41
92
69
66
39
50
48
84
90
35
84
81
88
11
58
82
14
16
27
64
01
04
24
63
99
99
09
88
18
31
81
91
99
85
18
34
09
25
51
25
47
07
71
64
37
95
62
45
46
76
18
39
54
91
10
46
72
72
94
52
26
68
53
63
58
32
25
21
42
20
96
66
99
09
52
54
46
65
39
05
81
54
28
63
75
01
89
07
81
37
69
36
04
28
00
95
13
02
30
43
21
96
08
05
01
24
52
59
76
00
18
06
76
96
29
57
96
51
70
78
95
11
94
32
91
52
91
15
66
89
31
06
09
66
15
57
53
00
86
33
20
14
48
55
79
45
36
31
98
46
13
30
68
18
63
90
98
77
10
22
43
58
66
95
70
78
32
72
00
15
01
52
01
32
18
76
98
65
51
42
24
40
19
21
69
13
92
24
45
43
00
90
38
04
77
93
81
44
75
36
03
59
45
96
64
13
96
62
64
08
59
43
68
38
73
92
67
53
83
22
85
17
17
89
42
86
31
19
79
47
08
99
11
13
78
84
29
43
35
08
13
67
16
67
54
88
39
05
12
09
72
00
10
36
71
50
62
83
13
02
12
91
13
67
06
15
93
32
87
07
50
90
90
16
78
45
25
85
49
79
05
33
03
76
13
19
15
66
91
94
86
20
53
20
64
80
50
06
45
17
65
42
45
84
98
31
06
17
37
81
70
57
83
92
70
05
68
69
51
52
74
48
50
77
56
44
67
94
23Closing prices, oldest first

Closing prices, oldest first

One per line, or CSV with a date and a close column; the last number on each line is used.

Rolling window (days)

Trading days per year

Try this

0 of 3 done

Read a regime change

Generate the calm-then-wild series and look at the rolling volatility chart.

What to look for: The rolling line sits near 12% for the first year and near 40% for the second, while the whole-sample number lands somewhere in between and describes neither year well.

One bad day

Generate the series with a crash and read the skewness and kurtosis.

What to look for: A single 12% drop makes the returns strongly left-skewed and fat-tailed. One day like that is what out-of-the-money puts are priced for.

Feed it back

Click the button to use the realised volatility as the contract volatility, then open the Black-Scholes page.

What to look for: Every pricing page now uses the measured number. Compare the option price with what it was at 20% and decide which one you would rather have paid.

Realised volatility

28.8%

504 prices, annualised

Implied volatility

20.0%

From the contract editor; ratio 0.69

Skewness / excess kurtosis

+0.09 / +2.70

A normal distribution has 0 and 0

Max drawdown

-31.9%

Worst peak-to-trough fall

The implied volatility is below what was realised: either the past was unusually rough, or options are cheap. The returns have fat tails, so a lognormal model understates the chance of big moves.

Volatility clusters: quiet stretches and wild stretches. Implied volatility is the market's forecast of where this line goes next, usually with a premium on top.

Black-Scholes assumes this is a bell curve. Real markets show fat tails, more days far from the middle than a normal distribution allows, which is what the smile is pricing.