Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm

Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

“…The mfBm models have been extensively studied in the literature [1][2][3][4][5][6][7][8][9]. Cheridito [2] derived an European call pricing option on an asset driven by a linear combination of a Brownian motion and an independent fractional Brownian motion.…”

“…One way to a more realistic modelling is to change the geometric Brownian motion to a geometric fractional Brownian motion: the dependence of the logreturn increments can now be modelled with the Hurst parameter of the fractional Brownian motion. It can be said that the properties of financial return series are nonnormal, nonindependent, and nonlinear, self-similar, with heavytails, in both autocorrelations and cross-correlations, and volatility clustering [2][3][4]. Since fractional Brownian motion has two substantial features such as self-similarity and longrange dependence, using it is more applicable to capture behavior from financial asset [3].…”

“…It can be said that the properties of financial return series are nonnormal, nonindependent, and nonlinear, self-similar, with heavytails, in both autocorrelations and cross-correlations, and volatility clustering [2][3][4]. Since fractional Brownian motion has two substantial features such as self-similarity and longrange dependence, using it is more applicable to capture behavior from financial asset [3]. Also, the fractional Brownian motion is neither a Markov process nor a semimartingale, and thus we cannot apply the common stochastic calculus to analyze it.…”

Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion

“…In the last few years, some articles have been published choosing fractional Brownian motion (fBm) as an underlying diffusive process (e.g., Refs. [7][8][9][14][15][16][17] and references therein). For example, Jiang et al [9] proposed a class of stochastic heat equations with first order fractional noises and established the existence and uniqueness of the solution of the equation.…”

“…Wang et al [15] studied the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fBm as a model of asset prices. Xiao et al [17] presented a pricing model for equity warrants in a mixed fractional Brownian environment and proposed a hybrid intelligent algorithm to solve the nonlinear optimization problem. Jańczak-Borkowska [8] investigated the existence and uniqueness of generalized backward stochastic differential equation driven by fBm with Hurst parameter H greater than 1/2, and shown the connection between this solution and the solution of parabolic partial differential equation with Neumann boundary condition.…”