Travelers 2009 Annual Report Download - page 239

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. The expected volatility is based on the
average historical volatility of the common stock of an industry peer group of entities, due to the
limited Company stock history, over the estimated option term based on the mid-month of the option
grant. 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 restriction on sale. A 10% discount, as measured by
the estimated cost of protecting against changes in market value, 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, 2009, 2008 and
2007:
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%
2008 Original Grants Reload Grants
Expected term of stock options . . . . . . . . . . . . 6 - 7 years 1 - 3 years
Expected volatility of the Company’s stock . . . . 22.8% - 29.9% 19.1% - 31.4%
Weighted average volatility . . . . . . . . . . . . . . . 23.1% 23.9%
Expected annual dividend per share . . . . . . . . . $1.16 - $1.20 $1.16 - $1.20
Risk-free rate . . . . . . . . . . . . . . . . . . . . . . . . . 2.61% - 3.75% 1.36% - 3.42%
2007 Original Grants Reload Grants
Expected term of stock options . . . . . . . . . . . . 6 - 7 years 1 - 3 years
Expected volatility of the Company’s stock . . . . 22.5% - 26.9% 14.3% - 19.7%
Weighted average volatility . . . . . . . . . . . . . . . 24.9% 16.5%
Expected annual dividend per share . . . . . . . . . $1.04 - $1.16 $1.04 - $1.16
Risk-free rate . . . . . . . . . . . . . . . . . . . . . . . . . 3.79% - 5.10% 3.34% - 5.06%
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