摘要
自相似性和长期相关性等分形特性已被认为是现代金融市场最具代表的特征,这使得分数布朗运动成为数理金融研究中更为合适的工具。文章通过假定股票价格服从几何分数布朗运动,构建了It^o型分数Black-Scholes市场;接着在分数风险中性测度下,利用随机微分方程和拟鞅(quasi-martingale)定价方法给出了分数Black-Scholes期权定价模型,使得原始的Black-Scholes公式仅成为其特例;最后借助推广的分数Clark-Clone公式,给出了分数欧式期权的套期保值策略。
The self-similarity and long-range dependence properties, which are regarded as the most representa-tive properties of modem financial market, make the fractional Brownian motion（FBM） a suitable tool in dif- ferent applications like mathematical finance. Under the hypotheses that the price follows geometric FBM, the Ito fractional Black-Scholes market is constructed. Using the stochastic differential equation and the quasi- martingale pricing method based on the fractional risk neutral measure, the fractional Black-Scholes model is solved, which makes the original Black-Scholes a specific example. Finally, by the generalized fractional Clark-Clone equation, the hedging strategy of fractional European option is presented.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第11期1388-1392,共5页
Journal of Hefei University of Technology：Natural Science
基金
江苏省高校哲学社会科学基金资助项目(2013SJB79004)
连云港市软科学资助项目(RK1203)
