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Share-based compensation (Tables)
 12 Months Ended
Dec. 31, 2019
Share-based Payment Arrangement [Abstract]  
Schedule of pre-tax and after-tax share-based compensation expense
The following table presents pre-tax and after-tax share-based compensation expense:
 
Year Ended December 31
 
(in millions of U.S. dollars)
2019

 
2018

 
2017

Stock options and shares issued under ESPP:
 
 
 
 
 
Pre-tax
$
42

 
$
50

 
$
41

After-tax (1)
$
39

 
$
40

 
$
26

Restricted stock:
 
 
 
 
 
Pre-tax
$
224

 
$
235

 
$
259

After-tax
$
180

 
$
178

 
$
151


(1) 
The windfall tax benefit recorded to Income tax expense in the Consolidated statement of operations was $12 million, $19 million, and $48 million for the years ended December 31, 2019, 2018, and 2017, respectively.
Schedule of the weighted-average model valuation assumptions
 
Year Ended December 31
 
 
2019

 
2018

 
2017

Dividend yield
2.2
%
 
2.0
%
 
2.0
%
Expected volatility
16.0
%
 
23.2
%
 
19.7
%
Risk-free interest rate
2.6
%
 
2.7
%
 
2.0
%
Expected life
5.7 years

 
5.7 years

 
5.8 years
Rollforward of the company's stock options
The following table presents a roll-forward of Chubb's stock options:
(Intrinsic Value in millions of U.S. dollars)
Number of Options

 
Weighted-Average Exercise Price

 
Weighted-Average Fair Value

 
Total Intrinsic Value

Options outstanding, December 31, 2016
10,180,720

 
$
87.29

 
 
 
 
Granted
2,079,522

 
$
139.00

 
$
22.97

 
 
Exercised
(1,632,629
)
 
$
73.53

 
 
 
$
111

Forfeited
(194,297
)
 
$
119.44

 
 
 
 
Options outstanding, December 31, 2017
10,433,316

 
$
99.20

 
 
 
 
Granted
1,842,690

 
$
143.07

 
$
29.71

 
 
Exercised
(1,065,384
)
 
$
73.57

 
 
 
$
71

Forfeited
(202,900
)
 
$
133.92

 
 
 
 
Options outstanding, December 31, 2018
11,007,722

 
$
108.25

 
 
 
 
Granted
2,073,940

 
$
133.90

 
$
18.76

 
 
Exercised
(1,944,604
)
 
$
84.13

 
 
 
$
122

Forfeited
(251,801
)
 
$
136.87

 
 
 
 
Options outstanding, December 31, 2019
10,885,257

 
$
116.79

 
 
 
$
423

Options exercisable, December 31, 2019
7,213,685

 
$
106.26

 
 
 
$
356
Rollforward of the company's restricted stock
The following table presents a roll-forward of our restricted stock awards. Included in the roll-forward below are 19,019 restricted stock awards, 20,784 restricted stock awards, and 22,013 restricted stock awards that were granted to non-management directors during the years ended December 31, 2019, 2018, and 2017, respectively:
 
Service-based
Restricted Stock Awards and Restricted Stock Units
 
 
Performance-based
Restricted Stock Awards
and Restricted Stock Units
 
 
Number of Shares

 
Weighted-Average Grant-Date Fair Value

 
Number of Shares

 
Weighted-Average Grant-Date Fair Value

Unvested restricted stock, December 31, 2016
5,805,126

 
$
109.39

 
931,169

 
$
111.17

Granted
1,707,094

 
$
139.18

 
267,282

 
$
138.90

Vested
(2,646,084
)
 
$
107.73

 
(222,954
)
 
$
113.30

Forfeited
(156,694
)
 
$
114.54

 
—

 
$
—

Unvested restricted stock, December 31, 2017
4,709,442

 
$
121.16

 
975,497

 
$
118.28

Granted
1,326,979

 
$
142.76

 
180,065

 
$
143.07

Vested
(2,545,090
)
 
$
114.83

 
(244,332
)
 
$
103.03

Forfeited
(196,482
)
 
$
131.06

 
—

 
$
—

Unvested restricted stock, December 31, 2018
3,294,849

 
$
134.17

 
911,230

 
$
127.27

Granted
1,492,900

 
$
134.38

 
212,059

 
$
133.90

Vested
(1,292,864
)
 
$
129.18

 
(196,640
)
 
$
115.62

Forfeited
(200,875
)
 
$
135.98

 
(50,437
)
 
$
132.36

Unvested restricted stock, December 31, 2019
3,294,010

 
$
136.20

 
876,212

 
$
131.16