scholarly journals Stock loan valuation based on the Finite Moment Log-Stable process

2018 ◽  
Vol 75 (2) ◽  
pp. 374-387 ◽  
Author(s):  
Congyin Fan ◽  
Kaili Xiang ◽  
Shanzhen Chen
Keyword(s):  
Stable Process ◽  
Finite Moment ◽  
Stock Loan

scholarly journals Pricing of Margin Call Stock Loan Based on the FMLS

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Kaili Xiang ◽  
Peng Hu ◽  
Xiao Li
Keyword(s):  
Free Boundary ◽  
Normal Distribution ◽  
Stock Price ◽  
Empirical Test ◽  
Stable Process ◽  
Standard Normal Distribution ◽  
Asymmetric Distribution ◽  
Finite Moment ◽  
The Impact ◽  
Stock Loan

In common stock loan, lenders face the risk that their loans will not be repaid if the stock price falls below loan, which limits the issuance and circulation of stock loans. The empirical test suggests that the log-return series of stock price in the US market reject the normal distribution and admit instead a subclass of the asymmetric distribution. In this paper, we investigate the model of the margin call stock loan problem under the assumption that the return of stock follows the finite moment log-stable process (FMLS). In this case, the pricing model of the margin call stock loan can be described by a space-fractional partial differential equation with a time-varying free boundary condition. We transform the free boundary problem to a linear complementarity problem, and the fully-implicit finite difference method that we used is unconditionally stable in both the integer and fractional order. The numerical experiments are carried out to demonstrate differences of the margin call stock loan model under the FMLS and the standard normal distribution. Last, we analyze the impact of key parameters in our model on the margin call stock loan evaluation and give some reasonable explanation.

scholarly journals Spectral risk measure of holding stocks in the long run

2020 ◽  
Vol 295 (1) ◽  
pp. 75-89
Author(s):  
Zsolt Bihary ◽  
Péter Csóka ◽  
Dávid Zoltán Szabó
Keyword(s):  
Stock Price ◽  
Risk Measures ◽  
Risk Measure ◽  
Stable Process ◽  
Important Special Case ◽  
Finite Moment ◽  
Holding Period ◽  
Long Run ◽  
Spectral Risk Measures ◽  
Spectral Risk Measure

AbstractWe investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock price follows specific processes, spectral risk becomes negative at long periods. We generalize this result for arbitrary exponential Lévy processes. We also prove the same behavior for all spectral risk measures (including the important special case of Expected Shortfall) when the stock price grows realistically fast and when it follows a geometric Brownian motion or a finite moment log stable process. This result would suggest that holding stocks for long periods has a vanishing downside risk. However, using realistic models, we find numerically that spectral risk initially increases for a significant amount of time and reaches zero level only after several decades. Therefore, we conclude that holding stocks has spectral risk for all practically relevant periods.

scholarly journals The Finite Moment Log Stable Process and Option Pricing

2003 ◽  
Vol 58 (2) ◽  
pp. 753-777 ◽  
Author(s):  
Peter Carr ◽  
Liuren Wu
Keyword(s):  
Option Pricing ◽  
Stable Process ◽  
Finite Moment

scholarly journals Numerical Method for a System of PIDEs Arising in American Contingent Claims under FMLS Model with Jump Diffusion and Regime-Switching Process

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Congyin Fan ◽  
Peimin Chen
Keyword(s):  
Numerical Method ◽  
Regime Switching ◽  
Stable Process ◽  
Jump Diffusion ◽  
Contingent Claims ◽  
State Variables ◽  
Finite Moment ◽  
Penalty Term ◽  
Optimal Exercise Boundary ◽  
Exercise Boundary

This paper investigates a numerical method for solving fractional partial integro-differential equations (FPIDEs) arising in American Contingent Claims, which follow finite moment log-stable process (FMLS) with jump diffusion and regime switching. Mathematically, the prices of American Contingent Claims satisfy a system of d problems with free-boundary values, where d is the number of regimes of the market. In addition, an optimal exercise boundary is needed to setup with each regime. Therefore, a fully implicit scheme based on the penalty term is arranged. In the end, numerical examples are carried out to verify the obtained theoretical results, and the impacts of state variables in our model on the optimal exercise boundary of American Contingent Claims are analyzed.

Depletion of coating color components in the blade coating process circulation

TAPPI Journal ◽  
2011 ◽  
Vol 10 (9) ◽  
pp. 17-23 ◽  
Author(s):  
ANNE RUTANEN ◽  
MARTTI TOIVAKKA
Keyword(s):  
Fine Particles ◽  
Particle Density ◽  
Stable Process ◽  
Size Fraction ◽  
Color Stability ◽  
Strong Interactions ◽  
Coating Process ◽  
Size Segregation ◽  
Coating Color ◽  
Average Size

Coating color stability, as defined by changes in its solid particle fraction, is important for runnability, quality, and costs of a paper coating operation. This study sought to determine whether the size or density of particles is important in size segregation in a pigment coating process. We used a laboratory coater to study changes in coating color composition during coating operations. The results suggest that size segregation occurs for high and low density particles. Regardless of the particle density, the fine particle size fraction (<0.2 μm) was the most prone for depletion, causing an increase in the average size of the particles. Strong interactions between the fine particles and other components also were associated with a low depletion tendency of fine particles. A stable process and improved efficiency of fine particles and binders can be achieved by controlling the depletion of fine particles.

STUDY OF INACCURACY IN THE OPERATION OF THE MAIN CONTROLLER OF STB MACHINE

2019 ◽  
Keyword(s):  
Normal Distribution ◽  
Stable Process ◽  
Random Errors ◽  
Actual Length ◽  
Experimental Data Processing ◽  
Set Up ◽  
Main Regulator ◽  
Transmission Gear ◽  
Selection Of

At production of fabrics, including fabrics for agricultural purpose, an important role is played by the cor-rect adjustment of operation of machine main regulator. The quality of setup of machine main controller is determined by the proper selection of rotation angle of warp beam weaving per one filling thread. In the pro-cess of using the regulator as a result of mistakes in adjustment, wear of transmission gear and backlashes in connections of details there are random changes in threads length. The purpose of the article is the research of property of random errors of basis giving by STB machine regulator. Mistakes can be both negative, and positive. In case of emergence only negative or only positive mistakes operation of the machine becomes im-possible as there will be a consecutive accumulation of mistakes. As a result of experimental data processing for stable process of weaving and the invariable diameter of basis threads winding of threads it is revealed that the random error of giving is set up as linear function of the accidental length having normal distribution. Measurements of accidental deviations in giving of a basis by the main regulator allowed to construct a curve of normal distribution of its actual length for one pass of weft thread. The presented curve of distribution of random errors in giving of a basis is the displaced curve of normal distribution of the accidental sizes. Also we define the density of probability of normal distribution of basis giving errors connected with a margin er-ror operation of the main regulator knowing of which allows to plan ways of their decrease that is important for improvement of quality of the produced fabrics.

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