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.

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.

scholarly journals Mathematical Model of Stock Prices via a Fractional Brownian Motion Model with Adaptive Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Tidarut Areerak
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Prices ◽  
Motion Model ◽  
Adaptive Parameters ◽  
Company Limited ◽  
Public Company ◽  
Proposed Model ◽  
Brownian Motion Model

The paper presents a mathematical model of stock prices using a fractional Brownian motion model with adaptive parameters (FBMAP). The accuracy index of the proposed model is compared with the Brownian motion model with adaptive parameters (BMAP). The parameters in both models are adapted at any time. The ADVANC Info Service Public Company Limited (ADVANC) and Land and Houses Public Company Limited (LH) closed prices are concerned in the paper. The Brownian motion model with adaptive parameters (BMAP) and fractional Brownian motion model with adaptive parameters (FBMAP) are applied to identify ADVANC and LH closed prices. The simulation results show that the FBMAP is more suitable for forecasting the ADVANC and LH closed price than the BMAP.

scholarly journals Pricing Vulnerable Options in a Mixed Fractional Brownian Motion with Jumps

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Panhong Cheng ◽  
Zhihong Xu
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Firm Value ◽  
Stock Price ◽  
Pricing Model ◽  
Mixed Fractional Brownian Motion ◽  
Actuarial Approach ◽  
Basic Parameters ◽  
Vulnerable Options ◽  
Economic Analyses

A new framework for pricing European vulnerable options is developed in the case where the underlying stock price and firm value follow the mixed fractional Brownian motion with jumps, respectively. This research uses the actuarial approach to study the pricing problem of European vulnerable options. An analytic closed-form pricing formula for vulnerable options with jumps is obtained. For the purpose of understanding the pricing model, some properties of this pricing model are discussed in the paper. Finally, we compare and analyze the pricing results of different pricing models and discuss the influences of basic parameters on the pricing results of our proposed model by using numerical simulations, and the corresponding economic analyses about these influences are given.

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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