Option contracts are probably stopped before expire dates and important events may cause jump of underlying assets price. The paper assumes that the two kinds of risks,caused by stochastic stopping and the jump of price, are nonsystematic. By means of no arbitrage capital asset pricing and Feynman-kac formula, it first studies stochastic lives exchange options pricing with the underlying assets obeying continuous diffusion processes and the underlying assets obeying jump-diffusion processes, and obtains corresponding pricing formulas. And then, it studies the stochastic life option pricing with the underlying asset obeying jump-diffusion process and interest rate being stochastic, and oblains corresponding pricing formula.