Based on a stochastic volatility and stochastic jump intensity ( SVSJ) option pricing model，this paper gives a thorough study of the S＆P 500 index options． The empirical results show that significant jump premiums only exist in short term out-of-the-money options and short term at-the-money options，and the jump premium is much larger than the volatility premium． With different model specifications，the paper finds that although the contribution of jump variances to the total variance is quite small，jump premium accounts for a large proportion of total risk premium． For all model specifications，all the model sperform better in high volatility periods than in low volatility periods． Among these models，the SVSJ model has the greatest pricing efficiency．