We　propose　a　semi-parametric　model　with　ARCH　disturbances　and　a　time-varying　parameter　in　the　mean　to　measure　risk　aversion.　Our　model　is　different　from　Chou　et　al.　(1992)　model　in　that　the　time-varying　price　of　volatility　is　a　nonparametric　function　depending　on　some　macroeconomic　factors　such　as　interest　rates.　Two　step　estimates　are　suggested　to　estimate　the　nonparametric　function　in　the　price　of　volatility　and　parameters　in　volatility,　in　which　the　first　step　estimate　is　based　on　local　linear　smoothing　and　the　second　step　estimate　on　the　maximum　likelihood　method.　Asymptotic　propertied　of　the　estimators　are　discussed,　and　the　simulation　shows　that　our　method　performs　well.