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Share-based compensation (Tables)
 12 Months Ended
Dec. 31, 2012
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)
2012

 
2011

 
2010

Stock options and shares issued under ESPP:
 
 
 
 
 
Pre-tax
$
22

 
$
23

 
$
28

After-tax (1)
$
17

 
$
17

 
$
20

Restricted stock:
 
 
 
 
 
Pre-tax
$
109

 
$
108

 
$
111

After-tax
$
64

 
$
70

 
$
79

 
 
 
 
 
 
Schedule of the weighted-average model valuation assumptions
The following table presents the weighted-average model assumptions used for grants:
 
Years Ended December 31
 
 
2012

2011

2010

Dividend yield
2.7
%
2.2
%
2.5
%
Expected volatility
29.8
%
28.8
%
30.3
%
Risk-free interest rate
1.1
%
2.3
%
2.5
%
Forfeiture rate
6.5
%
6.5
%
7.5
%
Expected life
5.8 years

5.4 years

5.4 years
Rollforward of the company's stock options
The following table presents a roll-forward of ACE'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, 2009
11,483,104

 
$
45.46

 
 
 
 
Granted
2,094,227

 
$
50.38

 
$
12.09

 
 
Exercised
(1,328,715
)
 
$
40.11

 
 
 
$
22

Forfeited
(305,723
)
 
$
49.77

 
 
 
 
Options outstanding, December 31, 2010
11,942,893

 
$
46.80

 
 
 
 
Granted
1,649,824

 
$
62.68

 
$
14.67

 
 
Exercised
(2,741,238
)
 
$
44.45

 
 
 
$
63

Forfeited
(271,972
)
 
$
51.33

 
 
 
 
Options outstanding, December 31, 2011
10,579,507

 
$
49.78

 
 
 
 
Granted
1,462,103

 
$
73.36

 
$
15.58

 
 
Exercised
(2,401,869
)
 
$
42.50

 
 
 
$
78

Forfeited
(190,082
)
 
$
61.87

 
 
 
 
Options outstanding, December 31, 2012
9,449,659

 
$
55.03

 
 
 
$
234

Options exercisable, December 31, 2012
6,446,407

 
$
50.26

 
 
 
$
190
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 25,669 restricted stock awards, 32,660 restricted stock awards, and 36,248 restricted stock awards that were granted to non-management directors during the years ended December 31, 2012, 2011, and 2010 respectively:
 
Number of Restricted Stock

 
Weighted-Average Grant-Date Fair Value

Unvested restricted stock, December 31, 2009
4,873,429

 
$
48.25

Granted
2,461,076

 
$
51.09

Vested
(1,771,423
)
 
$
50.79

Forfeited
(257,350
)
 
$
47.93

Unvested restricted stock, December 31, 2010
5,305,732

 
$
48.74

Granted
1,808,745

 
$
60.01

Vested
(1,929,189
)
 
$
50.82

Forfeited
(333,798
)
 
$
47.46

Unvested restricted stock, December 31, 2011
4,851,490

 
$
52.20

Granted
1,589,178

 
$
73.46

Vested
(1,923,385
)
 
$
52.71

Forfeited
(262,436
)
 
$
58.40

Unvested restricted stock, December 31, 2012
4,254,847

 
$
59.53