Asymptotic analysis for stochastic volatility: martingale expansion
Asymptotic analysis for stochastic volatility: martingale expansion
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DOI：
10.1007/s00780-010-0136-6
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发表时间：
2011-12-01
影响因子：
1.7
通讯作者：
Fukasawa, Masaaki
中科院分区：
文献类型：
--
作者：
Fukasawa, Masaaki
考虑了一类带跳的随机波动率模型，利用Yoshida鞅展开理论证明了欧式期权价格在Black-Scholes价格附近的渐近展开式.作为推论，得到了几个已知的正则和奇异扰动展开式公式。给出了Black-Scholes隐含波动率的一个扩展公式，解释了波动率偏置和期限结构。展开的首项总是对数货币性的仿射函数，而系数的期限结构取决于基础随机波动率模型的细节。几个具体的模型，代表各种类型的期限结构进行了研究。
A general class of stochastic volatility models with jumps is considered and an asymptotic expansion for European option prices around the Black-Scholes prices is validated in the light of Yoshida's martingale expansion theory. Several known formulas of regular and singular perturbation expansions are obtained as corollaries. An expansion formula for the Black-Scholes implied volatility is given which explains the volatility skew and term structure. The leading term of the expansion is always an affine function of log moneyness, while the term structure of the coefficients depends on the details of the underlying stochastic volatility model. Several specific models which represent various types of term structure are studied.