scholarly journals European Option Based on Least-Squares Method under Non-Extensive Statistical Mechanics

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 933
Author(s):  
Limin Liu ◽  
Yingying Cui
Keyword(s):  
Statistical Mechanics ◽  
Least Squares ◽  
Least Squares Method ◽  
Gaussian Model ◽  
Closed Form Solution ◽  
Least Square Method ◽  
Form Solution ◽  
Least Square ◽  
European Options ◽  
Non Gaussian

This paper is devoted to the study of the pricing of European options under a non-Gaussian model. This model follows a non-extensive statistical mechanics which can better describe the fractal characteristics of price movement in the financial market. Moreover, we present a simple but precise least-square method for approximation and obtain a closed-form solution of the price of European options. The advantages of this technique are illustrated by numerical simulation, which shows that the least-squares method is better compared with Borland’s two methods in 2002 and 2004.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

Solitary waves of the RLW equation via least squares method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ozlem Ersoy Hepson ◽  
Idris Dag ◽  
Bülent Saka ◽  
Buket Ay
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Spline Functions ◽  
Algebraic Equations ◽  
B Spline ◽  
B Splines ◽  
Rlw Equation ◽  
Set Up

Abstract Integration using least squares method in space and Crank–Nicolson approach in time is managed to set up an algorithm to solve the RLW equation numerically. Trial functions in the least square method consist of a combination of the quartic B-spline functions. Integration of the RLW equation gives a system of algebraic equations. The solutions consisting of a combination of the quartic B-splines are given for some initial and boundary value problems of RLW equation.

A New Method to Identify the Preisach Distribution Function of Hysteresis

2005 ◽  
Vol 475-479 ◽  
pp. 2107-2110 ◽  
Author(s):  
Fan Li ◽  
Jian Qin Mao ◽  
Hai Shan Ding ◽  
Wen Bo Zhang ◽  
Hui Bin Xu ◽  
...  
Keyword(s):  
Distribution Function ◽  
Least Squares ◽  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Least Squares Method ◽  
Input Sequence ◽  
Least Square Method ◽  
Least Square ◽  
New Method ◽  
Inference System

In this paper, a new method which combines the least square method with Tree-Structured fuzzy inference system is presented to approximate the Preisach distribution function. Firstly, by devising the input sequence and measure the output, discrete Preisach measure can be identified by the use of the least squares method. Then, the Preisach function can be obtained with Tree-Structured fuzzy inference system without any special smoothing means. So, this new method is not sensitive to noise, and is a universal approximator of the Preisach function. It collect the merit and overcome the deficiency of the existing methods.

scholarly journals Time Scale in Least Square Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Özgür Yeniay ◽  
Öznur İşçi ◽  
Atilla Göktaş ◽  
M. Niyazi Çankaya
Keyword(s):  
Least Squares ◽  
Time Scale ◽  
Least Squares Method ◽  
Least Square Method ◽  
Forward Direction ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Regression Equations ◽  
Nabla Derivative ◽  
Derivative Concept

Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.

An Application of Least Squares Method to the Solution of the Inverse Problem of Heat Conduction

1963 ◽  
Vol 85 (4) ◽  
pp. 378-379 ◽  
Author(s):  
Irving Frank
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Least Squares ◽  
Heat Input ◽  
Least Squares Method ◽  
Least Square Method ◽  
The Body ◽  
Least Square

When the temperature of a body at some point is known, it is generally possible to determine the rate of heat input to the surface of the body. However, when the temperatures are determined experimentally, it will be found that there is some uncertainty in the solution for the rate of heat input. It is suggested that a least square method be used to determine the rate of heat input which best fits the experimental data.

Segmented Auxiliary Power Model Based on Particle Swarm Optimization

2014 ◽  
Vol 1044-1045 ◽  
pp. 1321-1324
Author(s):  
Shao Chen Wu ◽  
Hai Sheng Liu ◽  
Fu Liang Deng
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Power Model ◽  
Segmentation Method ◽  
Method Of Least Squares ◽  
Swarm Optimization ◽  
Auxiliary Power ◽  
The Impact

The traditional modeling approach of auxiliary power is the least squares method, however, accuracy of the traditional least squares method is not high in fitting and forecasting, so we introduced segmentation method of least squares model, and consider the impact of many factors on the model ,proposed the improved least square method based on PSO. Application prove this method has a better fitting precision and predicition accuracy.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

Research on Generator Excitation Parameter Identification - PSS Low-Pass Link Parameter Identification

2013 ◽  
Vol 805-806 ◽  
pp. 716-720
Author(s):  
Tao Xu ◽  
Tian Long Shao ◽  
Dong Fang Zhang
Keyword(s):  
Mathematical Model ◽  
Parameter Identification ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
National Standards ◽  
Matlab Software ◽  
Low Pass ◽  
Newton Iterations ◽  
The Mathematical Model

Combined with the contents of the study-PSS low-pass link parameter identification. Least-squares method is selected. Using least-square method for PSS low-pass link mathematical model are also deduced. For the results, because of the mathematical model is solving nonlinear equations, cannot used by the Newton method directly. So we choose to use Newton iterations, with this feature, choose to use MATLAB software to solve the equation. Identification of the use of MATLAB software lags after the PSS parameters obtained recognition results compared with national standards, identifying and verifying the practicability.

Research on the Wire Drawing Die Pass Parameter Calculation Based on the Least Square Algorithm

2012 ◽  
Vol 591-593 ◽  
pp. 850-853
Author(s):  
Huai Xing Wen ◽  
Yong Tao Yang
Keyword(s):  
Pore Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Piecewise Linear ◽  
Wire Drawing ◽  
Least Square ◽  
Structure Characteristics ◽  
Drawing Die ◽  
The Wire ◽  
Drawing Dies

Drawing Dies meter A / D acquisition module will be collected from the mold hole contour data to draw a curve in Matlab. According to the mold pore structure characteristics of the curve, the initial cut-off point of each part of contour is determined and iteratived optimization to find the best cut-off point, use the least squares method for fitting piecewise linear and fitting optimization to find the function of the various parts of the curve function, finally calculate the pass parameters of drawing mode. Parameters obtained compare with the standard mold, both of errors are relatively small that prove the correctness of the algorithm. Also a complete algorithm flow of pass parameters is designed, it can fast and accurately measure the wire drawing die hole parameters.

A least squares method for earthquake mechanism determination using S-wave data

1964 ◽  
Vol 54 (6A) ◽  
pp. 2037-2047
Author(s):  
Agustin Udias
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Numerical Approach ◽  
Focal Mechanisms ◽  
Least Square ◽  
S Wave ◽  
Double Couple ◽  
Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

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