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Share-based compensation (Tables)
 12 Months Ended
Dec. 31, 2016
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)
2016

 
2015

 
2014

Stock options and shares issued under ESPP:
 
 
 
 
 
Pre-tax
$
33

 
$
31

 
$
28

After-tax (1)
$
20

 
$
21

 
$
19

Restricted stock:
 
 
 
 
 
Pre-tax
$
268

 
$
143

 
$
128

After-tax
$
167

 
$
84

 
$
75


(1) 
Excludes windfall tax benefit for share-based compensation recognized as a direct adjustment to Additional paid-in capital of $32 million, $26 million and $28 million for the years ended December 31, 2016, 2015 and 2014, respectively.
Schedule of the weighted-average model valuation assumptions
 
Year Ended December 31
 
 
2016

 
2015

 
2014

Dividend yield
2.3
%
 
2.3
%
 
2.7
%
Expected volatility
23.2
%
 
21.0
%
 
25.2
%
Risk-free interest rate
1.3
%
 
1.7
%
 
1.7
%
Expected life
5.6 years

 
5.8 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, 2013
9,496,856

 
$
61.84

 
 
 
 
Granted
1,782,903

 
$
96.77

 
$
18.00

 
 
Exercised
(1,511,948
)
 
$
54.84

 
 
 
$
73

Forfeited
(143,825
)
 
$
84.52

 
 
 
 
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

 
 
 
$
456

Options exercisable, December 31, 2016
6,562,884

 
$
72.90

 
 
 
$
389
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 23,812 restricted stock awards, 24,945 restricted stock awards, and 25,339 restricted stock awards that were granted to non-management directors during the years ended December 31, 2016, 2015, and 2014, 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, 2013
4,129,583

 
$
71.85

 
196,497

 
$
71.35

Granted
1,596,245

 
$
97.16

 
374,202

 
$
98.31

Vested
(1,500,949
)
 
$
68.33

 
(192,009
)
 
$
85.39

Forfeited
(387,782
)
 
$
73.21

 
—

 
$
—

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