基于波动率分解的期权定价

Option valuation based on volatility decomposition

文章通过将标的资产波动率分解为不相关的两个组成部分，构建了期权定价模型，并求解了相应的期权定价公式．分析新模型在标的资产收益率的偏度与峰度、隐含波动率等方面的重要特征，并利用市场数据对模型进行了拟合．研究表明：将波动率进行分解，以适应于其组件不同的运动过程，从而扩展了模型的适用场景；利用波动率组件的相互作用，即使在波动率参数较低时，也可以令短期期权获得明显的尖峰、波动率微笑等形态特征，从而有效地规避了单因素随机波动率模型的缺陷；同时，通过波动率分解引入新的风险源，模型具有更好的定价效率．

Through decomposing the volatility of underlying asset into two uncorrelated components, this article constructs a new option pricing model and resolves the option price formula. After analyzing skewness and kurtosis of underlying asset return, and studying implied volatility of option under the new model, this work calibrates model parameters using the market data. The result of study shows that new model can be suitable for volatility components with different evolution processes, it can generate substantial degree of excess kurtosis and depth of volatility smile even for options with short maturity, and it has more pricing effectiveness by introducing new risk factor.