Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
978900 | Physica A: Statistical Mechanics and its Applications | 2010 | 10 Pages |
Abstract
In this paper, in order to establish connection between fractional derivative and fractional Brownian motion (FBM), we first prove the validity of the fractional Taylor formula proposed by Guy Jumarie. Then, by using the properties of this Taylor formula, we derive a fractional Itô formula for H∈[1/2,1)H∈[1/2,1), which coincides in form with the one proposed by Duncan for some special cases, whose formula is based on the Wick Product. Lastly, we apply this fractional Itô formula to the option pricing problem when the underlying of the option contract is supposed to be driven by a geometric fractional Brownian motion. The case that the drift, volatility and risk-free interest rate are all dependent on tt is also discussed.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Lv Longjin, Fu-Yao Ren, Wei-Yuan Qiu,