Abstract: In order to illustrate why the mature stock index futures and option markets develop in parallel, this paper develops an expected utility maximization model to choose the optimal hedging alternatives when a fund company facing the stock market price change use the stock index futures and stock index option portfolios to avoid the risk. The main results are as follows: suppose that stock index futures and options markets are unbiased, a full hedge on stock index futures market is optimal and a stock index option is redundant; suppose that the stock index futures market is biased whereas the stock index options market is unbiased, a hedge on both stock index futures and options market is optimal and a stock index option is necessary. This conclusion gives evidence that China should continuously develop the index derivatives markets. Thus, it further suggests that with the steady operation of Shanghai-Shenzhen 300 stock index futures, China could launch the stock index options with the same underlying index in due time and form a pattern that stock index futures and option markets develop in parallel.