Travelers 2011 Annual Report Download - page 234

THE TRAVELERS COMPANIES, INC. AND SUBSIDIARIES
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (Continued)
12. SHARE-BASED INCENTIVE COMPENSATION (Continued)
The fair value of each option award is estimated on the date of grant by application of a variation
of the Black-Scholes option pricing model using the assumptions noted in the following table. The
expected term of newly granted stock options is the time to vest plus half the remaining time to
expiration. This considers the vesting restriction and represents an even pattern of exercise behavior
over the remaining term. Reload options are exercisable for the remaining term of the original option
and therefore would generally have a shorter expected term. Beginning in April 2010, due to the
Company having attained sufficient history with respect to changes in its stock prices over time, the
expected volatility assumption is based on the historical volatility of the Company’s common stock for
the same period as the estimated option term based on the mid-month of the option grant. Prior to
April 2010, the expected volatility was based on the average historical volatility of the common stock of
an industry peer group of entities due to the limited Company stock history. The expected dividend is
based upon the Company’s current quarter dividend annualized and assumed to be constant over the
expected option term. The risk-free interest rate for each option is the interpolated market yield for
the mid-month of the option grant on a U.S. Treasury bill with a term comparable to the expected
option term of the granted stock option. Shares received through option exercises under the reload
program are subject to either a one-year or two-year restriction on sale. A discount, as measured by the
estimated cost of protecting against changes in market value, 5% for one year sales restrictions and
10% for two year sales restrictions, has been applied to the fair value of reload options granted to
reflect these sales restrictions. The following assumptions were used in estimating the fair value of
options on grant date for the years ended December 31, 2011, 2010 and 2009:
2011 Original Grants Reload Grants
Expected term of stock options ............. 6 years 1 year
Expected volatility of the Company’s stock ..... 28.0% - 28.6% 15.7% - 17.6%
Weighted average volatility ................ 28.2% 15.9%
Expected annual dividend per share .......... $1.44 - $1.64 $1.44 - $1.64
Risk-free rate .......................... 1.19% - 2.62% 0.10% - 0.29%
2010 Original Grants Reload Grants
Expected term of stock options ............ 6 years 1 - 2 years
Expected volatility of the Company’s stock .... 28.3% - 29.1% 18.3% - 41.6%
Weighted average volatility ............... 28.4% 21.1%
Expected annual dividend per share ......... $1.32 - $1.44 $1.32 - $1.44
Risk-free rate ......................... 1.68% - 2.71% 0.20% - 0.95%
2009 Original Grants Reload Grants
Expected term of stock options ............ 6 years 1 - 2 years
Expected volatility of the Company’s stock .... 28.2% - 34.1% 36.5% - 55.1%
Weighted average volatility ............... 32.4% 42.9%
Expected annual dividend per share ......... $1.20 - $1.32 $1.20 - $1.32
Risk-free rate ......................... 2.07% - 2.85% 0.29% - 1.21%
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