Abstract: The randomness of interest and characteristics of fat-tailed, long-term dependence of return distribution of asset prices are considered. Thus, the distribution of Tsallis entropy, which has the characteristics of long-term memory and statistical feedback, is selected to describe the law of the asset prices movement. By using the actuarial approach method under the Vasicek interest rate model, the pricing formulas of power European options are obtained. The formulas not only generalize the classical Black-Scholes conclusion, but also contain the conclusions in the other literature.

Key words: Tsallis entropy, Vasicek interest rate model, power options, actuarial approach method