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中文摘要：
提出了一种从期权价格恢复标的资产隐含风险中性概率测度的新方法.在不完全市场条件下,运用高斯混合分布（GMD）构建了恢复最小距离隐含风险中性概率测度的数学优化模型,并进一步讨论模型的求解方法与技巧.采用欧式期权数据,通过数值实验对模型的有效性进行验证.实验结果表明,实际风险中性概率测度可由2个组成部分的高斯混合分布近似,形状更加具有尖峰性,且是双峰,左尾处含有一个较小峰值.这说明市场参与者对未来的预期集中度比较高,但市场对极端不利价格运动的预期（左尾部）比极端有利价格运动（右尾部）的预期要高,因此传统标的资产价格对数正态分布的假设会低估损失发生的可能性.
英文摘要：
A new approach to estimate the implied risk-neutral probability measure of the underlying assets from option prices is presented.Under incomplete market conditions,Gaussian mixture distribution（GMD） was used to construct the mathematical optimization model of restoring the minimum distance implied risk-neutral probability measure.Furthermore,solving methods and techniques of the optimization model were discussed.The effectiveness of the model was tested using European option data.The results show that the real risk-neutral probability measure can be approximated by the Gaussian mixture distribution of two components;the shape of it is more leptokurtic,being bimodal with a smaller peak at the left tail.This indicates that market participants expect the future with higher concentration.However,expectation for extremely unfavorable price movement（left tail） is higher than that for the extremely favorable price movement（right tail）,so traditional assumptions on the underlying asset with lognormal distribution would underestimate potential loss.
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