Abstract: Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are two main popular risk measurement tools presently. However, the present study on risk hedging problem with VaR (CVaR) is mostly carried out under specific distribution assumptions, which is prone to resulting in model risk and limiting its scope of application in practice. In addition, the traditional literature only defines risk reducing ratio as the risk hedging efficiency index, but different risk measure indices often induce inconsistent or even contradictory results. Therefore we need to seek a hedging efficiency index which is independent of risk measure indices. Method:To overcome the shortcomings above and improve existing results, the nonparametric kernel estimation method is introduced to estimate VaR and CVaR without a distribution assumption, and then the risk hedging model is constructed based on the VaR and CVaR kernel estimators, which can avoid the ex-ante model risk and parametric estimation error. In addition, expected utility theory is further applied to compare the hedging efficiency of risk-minimizing hedging strategies so as to avoid the inconsistent or even contradictory comparison results that are often induced by different risk decline ratios in traditional literatures.Data:The historical data of CSI 300 stock index and its futures is collected to test the theorem above. The data window ranges from April 16, 2010 to February 11, 2015, a total of 1172 daily data.Results:The empirical results based on CSI 300 index futures and spot market data show that four kinds of utility functions used by financial economics confirm consistently that minimum CVaR hedging strategy is more efficient than the minimum variance and the minimum VaR hedging strategies.Future research:The purpose of this paper is to provide a research framework which studies hedging problem under distribution uncertainty using kernel estimation method and expected utility theory. The research framework can be easily applied to hedging efficiency problem of other derivatives or other risk measure indices. So this paper provides a new research perspective for other scholar's related research.

Key words: risk hedging, expected utility, distributional uncertainty, kernel estimation