期刊
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
卷 16, 期 2, 页码 317-331出版社
SPRINGERNATURE
DOI: 10.2478/s13540-013-0020-0
关键词
fractional Brownian motion; stochastic stability; Black-Scholes model; large deviations; Hurst parameter
资金
- National Natural Science Foundation of China [11271139, 61104138]
- Guangdong Natural Science Foundation [S2011040001704]
- Foundation for Distinguished Young Talents in Higher Education of Guangdong, China [LYM10074]
- China Scholarship Council (CSC)
We deal with the stability problem of the fractional order Black-Scholes model driven by fractional Brownian motion (fBm). First, necessary and sufficient conditions are established for almost sure asymptotic stability and pth moment asymptotic stability by means of the largest Lyapunov exponent and the pth moment Lyapunov exponent, respectively. Moreover, we are able to present large deviations results for this fractional process. In particular, for the first time it is found that the Hurst parameter affects both stability conclusions and large deviations. Interestingly, large deviations always happen for the considered system when 1/2 < H < 1. This fact is due to the long-range dependence (LRD) property of the fBm. Numerical simulation results are presented to illustrate the above findings.
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