The compensation expenses were determined by calculating the fair value of each option grant using the Black-Scholes  option-pricing model. SENAO used the following weighted-average assumptions in calculating the fair value of the  options granted: Risk-free interest rate is based on the rate of the Taiwan government bonds in effect at the time of grant. Expected  volatilities are based on historical volatilities of stock prices of the similar company in the same industry and SENAO.  Expected life represents the period that SENAO’s share-based awards are expected to be outstanding and was determined  based on historical experience regarding similar awards, giving consideration to the contractual term of the share-based  awards. The dividend yield is zero as there are dividend protection rights in SENAO’s option plans with the exception  of the options granted in 2007. The expected dividend yield for SENAO’s 2007 Plan is based on anticipated future cash  dividends yield at the time of grant.  PART III F-75 (Continued) Year Ended December 31,  2011 Expected dividend yield 0%-1.49% Expected volatility 39.63%-49.88% Risk free interest rate 1.75%-2.00% Expected life 4.375 years December 31, 2010 Carrying Amount Unrealized Gain Unrealized Loss NT$ NT$ NT$ (In Millions) Available-for-sale securities Open-end mutual funds $  1,562 $  14 $  23 Domestic listed stocks 527 236 19 Corporate bonds 102 1 - 2,191 251 42 Held-to-maturity securities Corporate bond 9,868 326 96 Bank debentures 504 1 5 10,372 327 101 $  12,563 $  578 $  143 December 31, 2011 Carrying Amount Unrealized Gain Unrealized Loss NT$ NT$ NT$ (In Millions) Available-for-sale securities Open-end mutual funds $  2,137 $  77 $  9 Domestic listed stocks 343 55 54 Corporate bonds 77 1 - 2,557 133 63 c.  Marketable securities