The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial 'dynamically purified' price process that in theory allows to eliminate the impact of the stock price movements....

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num'eraire. It is shown that the presence of arbitrarily small stochastic deviations in the evolution of the num'eraire...

We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the sense that it is differentiable in mean square. We...