Muhannad Al-Saadony - Academia.edu (original) (raw)

Uploads

Thesis Chapters by Muhannad Al-Saadony

In this thesis, we consider some popular stochastic differential equation models used in finance,... more In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework.

Papers by Muhannad Al-Saadony

Journal of physics, May 1, 2021

In this article, we present that fractional Lévy processes which is very an important field in bo... more In this article, we present that fractional Lévy processes which is very an important field in both probability theory and its application in recent years. The fractional Brownian motion is suggested as the fractional Lévy processes in this article. We will make parameters estimate of the Vasicek process driven by fractional Brownian motion, that represented the short memory parameter (0 < H < ½) and the long memory parameter (½ < H < 1). So, Our aim is to study the behavior of stochastitc Vasicek Interest driven by fractional Brownian motion. We use maximum likelihood to estimate the drift, diffusion and Hurst parameters and generally the fractional Lévy processes. We illustrate our methods, and show the behavior of stochastic parameters using simulation and real data (ISX60).

Abbas [1] proposed new hierarchical representation of the adaptive Bayesian lasso model as unifor... more Abbas [1] proposed new hierarchical representation of the adaptive Bayesian lasso model as uniform density , mixing with standard exponential distribution based on a transformation of the mixture of uniform density and a particular gamma distribution formulation provided by Mallick & Yi [2] They consider the new proposed hierarchical formulation model and prior distributions, as well as the full Conditional posterior distributions structural under non conditioning on σ 2 which makes the uncertainty, of a unimodal full posterior, Conditioning on σ 2 is important, because it guarantees a unimodal full posterior Park and Casella [3]. So, we can conclude that [1] proposed new hierarchical representation utilizing a Nonscale mixture distributions, which needs to deal with this problem . To address this problem we consider new hierarchical representation of the adaptive Bayesian lasso for Tobit model based on scale mixture of Uniform density, mixing with standard exponential distribution.

In this article, we present that Black-Scholes process is a famous formula in financial mathemati... more In this article, we present that Black-Scholes process is a famous formula in financial mathematics. Our aim is to study the behavior of stochastic parameters in that model with application to Financial Time Stock Exchange FTSE100 Index. We use some parametric (Maximum likelihood, and Unbiased and Efficient) and nonparametric (Penalized least Squares, with different functions for the drift and diffusion coefficients and generally the Black-Scholes process) methods. Moreover, we study the change-point estimation for FTSE100 Index in order to determine these changes, and effects on the behavior of the Black-Scholes process.

Al-Qadisiyah Journal Of Pure Science, 2021

the model of term structure of interest rates are consider the most significant and computational... more the model of term structure of interest rates are consider the most significant and computationally difficult portion of the modern finance due to a relative complexity of using techniques. This article concerns the Bayesian estimation of interest rate models. Assume the short term interest rate follows the Cox Ingersoll Ross (CIR) process , this process has several feature. In particular mean reverting and the other feature is remanis non- negative , so this is what distinguishes it from previous models. It is implement in the R programing.

In this thesis, we consider some popular stochastic differential equation models used in finance,... more In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlying volatility process and of the unknown model parameters in the Heston model. The particle filter and the au...

The fractional Heston Model is a generalization of the Heston Model obtained by replacing Brownia... more The fractional Heston Model is a generalization of the Heston Model obtained by replacing Brownian motion by fractional Brownian motion in the two equations that define the Heston model. After defining the fractional Heston model and showing its representation as a Dynamic state space model, we will use that auxiliary particle filter both to sample the volatility process and to update the posterior distribution of the parameters sequentially as data arrive over time. We apply our approach to simulated and real data with success. Keywords:- Fractional Heston Model, maximum likelihood estimation, particle filter, auxiliary particle filter, sequential Bayesian inference.

International Journal of Statistics and Probability, 2013

Al-Qadisiyah Journal Of Pure Science, 2021

Right-tailed distributions are very important in many applications. There are many studies estima... more Right-tailed distributions are very important in many applications. There are many studies estimating the tail index. In this paper, we will estimate the tail parameter using the three (the Direct, Bootstrap and Double Bootstrap) methods. Our aim is to illustrate the best way to estimate the -stable with using simulation and real data for the daily Iraqi financial market dataset.

Bayesian Stochastic Differential Equation Modelling with Application to Finance Muhannad Al-Saado... more Bayesian Stochastic Differential Equation Modelling with Application to Finance Muhannad Al-Saadony Abstract In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlyi...

In this article, we present that Black-Scholes process is a famous formula in financial mathemati... more In this article, we present that Black-Scholes process is a famous formula in financial mathematics. Our aim is to study the behavior of stoachastic parameters in that model with application to Financial Time Stock Exchange FTSE100 Index. We use some parametric (Maximum likelihood, and Unbiased and Effi-cent) and nonparametric (Penalized least Squares, with different functions for the drift and diffusion coefficients and generally the Black-Scholes process) estimations. We study the change-point estimation of FSTE100 Index in order to determine these changes, and effects on the behavior of the Black-Scholes process.

This paper concerns the estimation of parameters in the "Vasicek Interest Rate" model under a Bay... more This paper concerns the estimation of parameters in the "Vasicek Interest Rate" model under a Bayesian framework. These popular models are challenging to fit with Markov chain Monte Carlo (McMC) methods as the structure of the model leads to considerable autocorrelation in the chains. Accordingly, we demonstrate that a simple reparameterisation using the Cholesky decomposition can greatly improves the performance of the McMC algorithm and hence lead to valid Bayesian inference on the Vasicek model.

In this thesis, we consider some popular stochastic differential equation models used in finance,... more In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework.

Journal of physics, May 1, 2021

In this article, we present that fractional Lévy processes which is very an important field in bo... more In this article, we present that fractional Lévy processes which is very an important field in both probability theory and its application in recent years. The fractional Brownian motion is suggested as the fractional Lévy processes in this article. We will make parameters estimate of the Vasicek process driven by fractional Brownian motion, that represented the short memory parameter (0 < H < ½) and the long memory parameter (½ < H < 1). So, Our aim is to study the behavior of stochastitc Vasicek Interest driven by fractional Brownian motion. We use maximum likelihood to estimate the drift, diffusion and Hurst parameters and generally the fractional Lévy processes. We illustrate our methods, and show the behavior of stochastic parameters using simulation and real data (ISX60).

Abbas [1] proposed new hierarchical representation of the adaptive Bayesian lasso model as unifor... more Abbas [1] proposed new hierarchical representation of the adaptive Bayesian lasso model as uniform density , mixing with standard exponential distribution based on a transformation of the mixture of uniform density and a particular gamma distribution formulation provided by Mallick & Yi [2] They consider the new proposed hierarchical formulation model and prior distributions, as well as the full Conditional posterior distributions structural under non conditioning on σ 2 which makes the uncertainty, of a unimodal full posterior, Conditioning on σ 2 is important, because it guarantees a unimodal full posterior Park and Casella [3]. So, we can conclude that [1] proposed new hierarchical representation utilizing a Nonscale mixture distributions, which needs to deal with this problem . To address this problem we consider new hierarchical representation of the adaptive Bayesian lasso for Tobit model based on scale mixture of Uniform density, mixing with standard exponential distribution.

In this article, we present that Black-Scholes process is a famous formula in financial mathemati... more In this article, we present that Black-Scholes process is a famous formula in financial mathematics. Our aim is to study the behavior of stochastic parameters in that model with application to Financial Time Stock Exchange FTSE100 Index. We use some parametric (Maximum likelihood, and Unbiased and Efficient) and nonparametric (Penalized least Squares, with different functions for the drift and diffusion coefficients and generally the Black-Scholes process) methods. Moreover, we study the change-point estimation for FTSE100 Index in order to determine these changes, and effects on the behavior of the Black-Scholes process.

Al-Qadisiyah Journal Of Pure Science, 2021

the model of term structure of interest rates are consider the most significant and computational... more the model of term structure of interest rates are consider the most significant and computationally difficult portion of the modern finance due to a relative complexity of using techniques. This article concerns the Bayesian estimation of interest rate models. Assume the short term interest rate follows the Cox Ingersoll Ross (CIR) process , this process has several feature. In particular mean reverting and the other feature is remanis non- negative , so this is what distinguishes it from previous models. It is implement in the R programing.

In this thesis, we consider some popular stochastic differential equation models used in finance,... more In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlying volatility process and of the unknown model parameters in the Heston model. The particle filter and the au...

The fractional Heston Model is a generalization of the Heston Model obtained by replacing Brownia... more The fractional Heston Model is a generalization of the Heston Model obtained by replacing Brownian motion by fractional Brownian motion in the two equations that define the Heston model. After defining the fractional Heston model and showing its representation as a Dynamic state space model, we will use that auxiliary particle filter both to sample the volatility process and to update the posterior distribution of the parameters sequentially as data arrive over time. We apply our approach to simulated and real data with success. Keywords:- Fractional Heston Model, maximum likelihood estimation, particle filter, auxiliary particle filter, sequential Bayesian inference.

International Journal of Statistics and Probability, 2013

Al-Qadisiyah Journal Of Pure Science, 2021

Right-tailed distributions are very important in many applications. There are many studies estima... more Right-tailed distributions are very important in many applications. There are many studies estimating the tail index. In this paper, we will estimate the tail parameter using the three (the Direct, Bootstrap and Double Bootstrap) methods. Our aim is to illustrate the best way to estimate the -stable with using simulation and real data for the daily Iraqi financial market dataset.

Bayesian Stochastic Differential Equation Modelling with Application to Finance Muhannad Al-Saado... more Bayesian Stochastic Differential Equation Modelling with Application to Finance Muhannad Al-Saadony Abstract In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlyi...

In this article, we present that Black-Scholes process is a famous formula in financial mathemati... more In this article, we present that Black-Scholes process is a famous formula in financial mathematics. Our aim is to study the behavior of stoachastic parameters in that model with application to Financial Time Stock Exchange FTSE100 Index. We use some parametric (Maximum likelihood, and Unbiased and Effi-cent) and nonparametric (Penalized least Squares, with different functions for the drift and diffusion coefficients and generally the Black-Scholes process) estimations. We study the change-point estimation of FSTE100 Index in order to determine these changes, and effects on the behavior of the Black-Scholes process.

This paper concerns the estimation of parameters in the "Vasicek Interest Rate" model under a Bay... more This paper concerns the estimation of parameters in the "Vasicek Interest Rate" model under a Bayesian framework. These popular models are challenging to fit with Markov chain Monte Carlo (McMC) methods as the structure of the model leads to considerable autocorrelation in the chains. Accordingly, we demonstrate that a simple reparameterisation using the Cholesky decomposition can greatly improves the performance of the McMC algorithm and hence lead to valid Bayesian inference on the Vasicek model.