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Share-based compensation (Tables)
 12 Months Ended
Dec. 31, 2015
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:
 
Years Ended December 31
 
(in millions of U.S. dollars)
2015

 
2014

 
2013

Stock options and shares issued under ESPP:
 
 
 
 
 
Pre-tax
$
31

 
$
28

 
$
24

After-tax (1)
$
21

 
$
19

 
$
18

Restricted stock:
 
 
 
 
 
Pre-tax
$
143

 
$
128

 
$
153

After-tax
$
84

 
$
75

 
$
89


(1) 
Excludes windfall tax benefit for share-based compensation recognized as a direct adjustment to Additional paid-in capital of $26 million, $28 million and $36 million for the years ended December 31, 2015, 2014 and 2013, respectively.
Schedule of the weighted-average model valuation assumptions
 
Years Ended December 31
 
 
2015

2014

2013

Dividend yield
2.3
%
2.7
%
2.4
%
Expected volatility
21.0
%
25.2
%
27.8
%
Risk-free interest rate
1.7
%
1.7
%
1.0
%
Expected life
5.8 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, 2012
9,449,659

 
$
55.03

 
 
 
 
Granted
1,821,063

 
$
85.41

 
$
17.29

 
 
Exercised
(1,658,671
)
 
$
48.17

 
 
 
$
70

Forfeited
(115,195
)
 
$
72.50

 
 
 
 
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

 
 
 
$
379

Options exercisable, December 31, 2015
6,424,800

 
$
64.45

 
 
 
$
337
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 24,945 restricted stock awards, 25,339 restricted stock awards, and 20,969 restricted stock awards that were granted to non-management directors during the years ended December 31, 2015, 2014, and 2013, respectively:
 
Service-based
Restricted Stock Awards
 
 
Performance-based
Restricted Stock Awards
 
 
Number of Shares

 
Weighted-Average Grant-Date Fair Value

 
Number of Shares

 
Weighted-Average Grant-Date Fair Value

Unvested restricted stock, December 31, 2012
4,015,732

 
$
59.51

 
239,115

 
$
59.94

Granted
1,347,679

 
$
85.61

 
196,806

 
$
89.90

Vested
(1,715,414
)
 
$
54.97

 
(236,080
)
 
$
75.29

Forfeited
(136,307
)
 
$
67.68

 
(3,344
)
 
$
69.39

Unvested restricted stock, December 31, 2013
3,511,690

 
$
71.42

 
196,497

 
$
71.35

Granted
1,295,734

 
$
97.04

 
374,202

 
$
98.31

Vested
(1,468,894
)
 
$
68.00

 
(192,009
)
 
$
85.39

Forfeited
(145,012
)
 
$
81.73

 
—

 
$
—

Unvested restricted stock, December 31, 2014
3,193,518

 
$
82.91

 
378,690

 
$
90.87

Granted
1,124,143

 
$
114.28

 
326,860

 
$
113.29

Vested
(1,299,895
)
 
$
79.49

 
(110,340
)
 
$
98.70

Forfeited
(192,009
)
 
$
95.54

 
—

 
$
—

Unvested restricted stock, December 31, 2015
2,825,757

 
$
96.10

 
595,210

 
$
101.73