Numerically pricing American options under the generalized mixed fractional Brownian motion model

2016 ◽  
Vol 451 ◽  
pp. 180-189 ◽  
Author(s):  
Wenting Chen ◽  
Bowen Yan ◽  
Guanghua Lian ◽  
Ying Zhang
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
American Options ◽  
Motion Model ◽  
Mixed Fractional Brownian Motion ◽  
Brownian Motion Model

OPTION PRICING FOR PROCESSES DRIVEN BY MIXED FRACTIONAL BROWNIAN MOTION WITH SUPERIMPOSED JUMPS

2015 ◽  
Vol 29 (4) ◽  
pp. 589-596 ◽  
Author(s):  
B.L.S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Option Price ◽  
Motion Model ◽  
Price Process ◽  
European Call Option ◽  
Mixed Fractional Brownian Motion ◽  
Special Cases ◽  
Brownian Motion Model

We propose a geometric mixed fractional Brownian motion model for the stock price process with possible jumps superimposed by an independent Poisson process. Option price of the European call option is computed for such a model. Some special cases are studied in detail.

Pricing Model for Convertible Bonds: A Mixed Fractional Brownian Motion with Jumps

2015 ◽  
Vol 5 (3) ◽  
pp. 222-237 ◽  
Author(s):  
Jie Miao ◽  
Xu Yang
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Empirical Study ◽  
Fractional Brownian Motion ◽  
Conditional Expectation ◽  
Convertible Bonds ◽  
Motion Model ◽  
Pricing Model ◽  
Mixed Fractional Brownian Motion ◽  
Brownian Motion Model

AbstractA mathematical model to price convertible bonds involving mixed fractional Brownian motion with jumps is presented. We obtain a general pricing formula using the risk neutral pricing principle and quasi-conditional expectation. The sensitivity of the price to changing various parameters is discussed. Theoretical prices from our jump mixed fractional Brownian motion model are compared with the prices predicted by traditional models. An empirical study shows that our new model is more acceptable.

scholarly journals Stochastic Fractal Dimension Image

2009 ◽  
Author(s):  
Nicholas J. Tustison ◽  
James Gee
Keyword(s):  
Brownian Motion ◽  
Fractal Dimension ◽  
Fractional Brownian Motion ◽  
Fractal Analysis ◽  
Medical Image ◽  
Fractal Theory ◽  
Motion Model ◽  
Edge Enhancement ◽  
Brownian Motion Model ◽  
Medical Image Classification

Fractal analysis for medical image classification and analysis was introduced in cite{Chen1989}. According to the authors, when viewed as an intensity surface, Mandelbrot's fractal theory provides an informative framework for characterizing such a surface. Using the fractional Brownian motion model, the authors provide an algorithm for converting a scalar image to a fractal dimension image for classification purposes or edge enhancement. This submission constitutes a report on the ITK implementation of this algorithm.

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