Communications in Information and Systems
Volume 15 (2015)
Stochastic volatility models with volatility driven by fractional Brownian motions
Pages: 47 – 55
In this paper the price of a risky asset that has a stochastic volatility being a function of a fractional Brownian motion is considered. Such models can provide a long range dependence for the volatility. The probability density function for the price at a given time is given explicitly under some natural, verifiable conditions. An option pricing model is also considered with some explicit results.
stochastic volatility, fractional Brownian motion, financial models
2010 Mathematics Subject Classification
60H30, 91B25, 91G20, 91G80