Fractional Brownian motion (fBm) can be introduced by a moving average representation driven by standard Brownian motion, which is an affine Markov process. Motivated by this we aim at results analogous to those achieved in recent years for affine models. Using a simple prediction formula for the conditional expectation of a fBm and its Gaussianity, we calculate the conditional characteristic functions of fBm and related processes, including important examples like fractional Ornstein-Uhlenbeck- or Cox-Ingersoll-Ross processes. As an application we propose a fractional Vasicek bond market model and compare prices of zero coupon bonds to those achieved in the classical Vasicek case.    «

Fractional Brownian motion (fBm) can be introduced by a moving average representation driven by standard Brownian motion, which is an affine Markov process. Motivated by this we aim at results analogous to those achieved in recent years for affine models. Using a simple prediction formula for the conditional expectation of a fBm and its Gaussianity, we calculate the conditional characteristic functions of fBm and related processes, including important examples like fractional Ornstein-...    »