Fractional Brownian Motion


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Fractional Brownian Motion

A biased random walk. Unlike Standard Brownian Motion, the odds are biased in one direction or the other. It is like playing with loaded dice.

Fractional Brownian Motion

A random walk with some bias. That is, fractional Brownian motion means that a security's price moves seemingly randomly, but with some external event sending it in one direction or the other.
References in periodicals archive ?
Yang, "The pricing of vulnerable options in a fractional brownian motion environment," Discrete Dynamics in Nature and Society, vol.
A Gaussian stochastic process [([B.sup.H.sub.t]).sub.t[greater than or equal to]0] of Hurst parameter H [member of] (0,1) is called (standard) fractional Brownian motion, if
Mixed Jump-Diffusion Fractional Brownian Motion Pricing Model and Wick-Ito-Skorohod Integral
By comparison between theoretical and empirical prices, Figure 4 shows pricing errors under the pricing model of lookback option with transaction costs based on fractional Brownian motion process (H = 0.7) and Black-Scholes model, respectively.
In this paper, Asian option pricing problems with transaction costs and dividends under fractional Brownian motion are studied.
[sigma] is volatility; [B.sub.t.sup.H] is a fractional Brownian motion with Hurst parameter H [member of] (0, 1) which is Centered Gaussian process with mean zero and covariance cov [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]: [Q.sub.t] is a poisson process with intensity [lambda], dependent of [B.sub.t.sup.H], Nt is Poisson compensation process and equals [Q.sub.t] - [lambda] t.
[6] Mandelbrot, B.B., Van Ness, J.W., Fractional Brownian Motion. Fractional noises and Applications, SIAM Review, Vol.
In the case of nonlocality in time anomalous diffusion is often connected with one of the two prominent underlying stochastic processes, namely, continuous-time random walks [23] and fractional Brownian motion [15].
A Fractional Brownian Motion (FBM) (Vasconcelos 2004), is a Gaussian process s{[W.sub.H](t), t > 0} with zero mean and stationary increments whose variance and covariance are given by
Most books about fractional Brownian motion focus on probabilistic properties, says Prakasa Rao (mathematics and statistics, U.
"A Class of Micropulses and Anti-persistent Fractional Brownian Motion," Stochastic Processes and Their Applications, 60, 1, January, 1995, pp.
These characteristics are different from standard Brownian motion but similar to fractional Brownian motion. All of these features make fractional Brownian motion more widely used in assets pricing.

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