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基于Tsallis分布及跳扩散过程的欧式期权定价

, PP. 41-48

Keywords: Tsallis熵,期权定价,,反常扩散

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Abstract:

?准确描述资产价格的运行规律是进行衍生产品定价及风险控制的基础。受金融市场外部环境的影响,资产收益率常常具有尖峰厚尾和偏尾的现象,为了准确地描述资产价格的运动规律,本文利用具有长程记忆及统计反馈性质的Tsallis熵分布和一类更新过程,建立了跳-反常扩散的股票价格运动模型。利用随机微分和鞅方法,在风险中性的条件下,得到了欧式期权的定价公式,该公式推广了文献11和21的相应结论。最后,利用上证指数数据分别计算出了各模型的参数以及对资产收益率拟合的平均绝对误差,数据分析结果表明本文模型与文献11和21相比其平均绝对误差分别减小了10.4%和25.1%。说明了本文模型对资产收益率尖峰厚尾及偏尾等现象的捕捉更为准确。

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