调和稳定Lévy过程驱动的双重跳跃模型及期权应用

Option Pricing of A Double Jump Model Driven by Tempered Stable Lévy Processes and Its Application

为准确刻画证券价格波动过程中的跳跃特征,捕获收益率尖峰厚尾、有偏等非高斯特征以及波动率集聚、异方差性等效应,建立了证券价格与相应波动率均存在跳跃的随机波动率模型,其中跳跃分布为两类纯跳跃Lévy分布(调和稳定分布和速降调和稳定分布)。最终,构建得到调和稳定Lévy过程驱动的双重跳跃随机波动模型。利用恒生和标普500股指数据进行实证,结果表明:与仿射跳扩散相比,纯跳跃Lévy分布能捕获随机信息的尖峰厚尾特征,拟合能力更优越,股指收益尾部分布存在速降特征。在此基础上的期权定价结果表明,速降调和稳定过程驱动的双重跳跃随机波动模型更有效。

In order to characterize the jump feature of securities price and the associated volatility process, which involves the leptokurtosis, heavy tailed and skewed non-Gaussian phenomena in stock returns, as well to simultaneously address the volatility clustering and heteroskedasticity effect, this paper introduces two pure jump Levy processes （classical tempered stable and rapidly decreasing tempered stable processes） into the double jump stochastic volatility model in which both the returns and volatility processes jumps. Thus we establish double jump stochastic volatility models driven by tempered stable L;vy processes. The empirical studies of hang Seng and SP 500 index show that, compared with affine jump diffusion processes, pure jump Levy distribution models can capture the above-mentioned characteristics more accurately and the tail distribution of stock index returns express rapidly decreasing phenomenon. Option pricing results demonstrate that the double jump stochastic volatility model driven by rapidly decreasing tempered stable process is more effective.