Option pricing is mainly based on ideal market conditions which are well represented by the Geometric Brownian Motion (GBM) as market model. We study the effect of non-ideal market conditions on the price of the option. We focus our attention on two crucial aspects appearing in real markets: The influence of heavy tails and the effect of colored noise. We will see that both effects have opposit...

Fundamental to many applications in financial engineering is the normal (Gaussian) distribution. It is the building block for simulating such basic stochastic processes as Brownian motion and geometric Brownian motion. In this section, we will go over algorithms for generating univariate normal rvs and learn how to use such algorithms for constructing sample paths of Brownian motion and geometr...

Fundamental to many applications in financial engineering is the normal (Gaussian) distribution. It is the building block for simulating such basic stochastic processes as Brownian motion and geometric Brownian motion. In this section, we will go over algorithms for generating univariate normal rvs and learn how to use such algorithms for constructing sample paths of Brownian motion and geometr...

The geometric Brownian motion (GBM) model is a mathematical that has been used to asset price paths. By incorporating Hurst parameter GBM characterize long-memory phenomenon, the fractional (GFBM) was introduced, which allows its disjoint increments be correlated. This paper investigates accuracy of and GFBM in modelling Malaysia’s crude palm oil simulation, see display persistent or anti-persi...

The Geometric Brownian motion (GBM) is a standard method for modeling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, GBM has been considered unable to properly capture important features, like extreme behaviour or volatility clustering. We propose an approach by which, the parameters of the GBM follow...

We study the numerical evaluation of several functions appearing in small time expansion distribution time-integral geometric Brownian motion as well its joint with terminal value underlying motion. A precise these distributions is relevant for simulation stochastic volatility models log-normally distributed volatility, and Asian option pricing Black-Scholes model. derive series expansions dist...