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.