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Share-based compensation (Tables)
 12 Months Ended
Dec. 31, 2017
Disclosure of Compensation Related Costs, Share-based Payments [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)
2017

 
2016

 
2015

Stock options and shares issued under ESPP:
 
 
 
 
 
Pre-tax
$
41

 
$
33

 
$
31

After-tax (1)
$
26

 
$
20

 
$
21

Restricted stock:
 
 
 
 
 
Pre-tax
$
259

 
$
268

 
$
143

After-tax
$
151

 
$
167

 
$
84


(1) 
Excludes windfall tax benefit for share-based compensation recognized as a direct adjustment to Additional paid-in capital of $32 million and $26 million for the years ended December 31, 2016 and 2015, respectively. Due to the adoption of new accounting guidance, windfall tax benefits for share-based compensation beginning in 2017 are recognized through Net income rather than Additional paid-in capital. The excess tax benefit recorded to Income tax expense in the Consolidated statement of operations was $48 million for the year ended December 31, 2017.
Schedule of the weighted-average model valuation assumptions
 
Year Ended December 31
 
 
2017

 
2016

 
2015

Dividend yield
2.0
%
 
2.3
%
 
2.3
%
Expected volatility
19.7
%
 
23.2
%
 
21.0
%
Risk-free interest rate
2.0
%
 
1.3
%
 
1.7
%
Expected life
5.8 years

 
5.6 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, 2014
9,623,986

 
$
69.06

 
 
 
 
Granted
1,892,641

 
$
114.78

 
$
18.49

 
 
Exercised
(1,457,580
)
 
$
60.88

 
 
 
$
72

Forfeited
(205,551
)
 
$
100.25

 
 
 
 
Options outstanding, December 31, 2015
9,853,496

 
$
78.40

 
 
 
 
Assumed in Chubb Corp Acquisition
339,896

 
$
77.83

 
$
36.07

 
 
Granted
1,929,616

 
$
118.39

 
$
21.52

 
 
Exercised
(1,728,949
)
 
$
66.65

 
 
 
$
99

Forfeited
(213,339
)
 
$
110.01

 
 
 
 
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

 
 
 
$
490

Options exercisable, December 31, 2017
6,675,491

 
$
82.59

 
 
 
$
424
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 22,013 restricted stock awards, 23,812 restricted stock awards, and 24,945 restricted stock awards that were granted to non-management directors during the years ended December 31, 2017, 2016, and 2015, 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, 2014
3,837,097

 
$
83.60

 
378,690

 
$
90.87

Granted
1,417,965

 
$
114.37

 
326,860

 
$
113.29

Vested
(1,341,358
)
 
$
80.05

 
(110,340
)
 
$
98.70

Forfeited
(424,535
)
 
$
87.36

 
—

 
$
—

Unvested restricted stock, December 31, 2015
3,489,169

 
$
97.01

 
595,210

 
$
101.73

Assumed in Chubb Corp Acquisition
3,706,639

 
$
111.02

 
—

 
$
—

Granted
1,622,065

 
$
118.70

 
517,507

 
$
118.96

Vested
(2,592,622
)
 
$
100.87

 
(181,548
)
 
$
102.43

Forfeited
(420,125
)
 
$
109.42

 
—

 
$
—

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
4,709,422

 
$
121.16

 
975,497

 
$
118.28