scholarly journals Development of Computational Algorithms for Evaluating Option Prices Associated with Square-Root Volatility Processes

2008 ◽  
Vol 11 (4) ◽  
pp. 687-703
Author(s):  
Hideyuki Takada ◽  
Ushio Sumita ◽  
Hui Jin
Keyword(s):  
Computational Algorithms ◽  
Square Root ◽  
Option Prices

CONVERGENCE SPEED OF GARCH OPTION PRICE TO DIFFUSION OPTION PRICE

2009 ◽  
Vol 12 (03) ◽  
pp. 359-391 ◽  
Author(s):  
JIN-CHUAN DUAN ◽  
YAZHEN WANG ◽  
JIAN ZOU
Keyword(s):  
Discrete Time ◽  
Option Price ◽  
Garch Model ◽  
Convergence Speed ◽  
Time Interval ◽  
Square Root ◽  
Option Prices ◽  
European Option ◽  
The Garch Model

It is well known that as the time interval between two consecutive observations shrinks to zero, a properly constructed GARCH model will weakly converge to a bivariate diffusion. Naturally the European option price under the GARCH model will also converge to its bivariate diffusion counterpart. This paper investigates the convergence speed of the GARCH option price. We show that the European option prices under the two corresponding models are equal up to an order near the square root of the length of discrete time interval.

A REGULARIZED FOURIER TRANSFORM APPROACH FOR VALUING OPTIONS UNDER STOCHASTIC DIVIDEND YIELDS

2010 ◽  
Vol 13 (02) ◽  
pp. 211-240 ◽  
Author(s):  
BAYE M. DIA
Keyword(s):  
Fourier Transform ◽  
Option Pricing ◽  
Inverse Fourier Transform ◽  
Option Price ◽  
Square Root ◽  
Option Prices ◽  
European Options ◽  
Dividend Yield ◽  
New Approach ◽  
Main Effects

This paper studies the option pricing problem in a class of models in which dividend yields follow a time-homogeneous diffusion. Within this framework, we develop a new approach for valuing options based on the use of a regularized Fourier transform. We derive a pricing formula for European options which gives the option price in the form of an inverse Fourier transform and propose two methods for numerically implementing this formula. As an application of this pricing approach, we introduce the Ornstein-Uhlenbeck and the square-root dividend yield models in which we explicitly solve the pricing problem for European options. Finally we highlight the main effects of a stochastic dividend yield on option prices.

About the Complexity of Square Root Extraction Algorithms in Finite Fields and Residue Rings

Vestnik MEI ◽  
2018 ◽  
Vol 5 (5) ◽  
pp. 79-88
Author(s):  
Sergey B. Gashkov ◽  
◽  
Aleksandr B. Frolov ◽  
Elizaveta Р. Popova ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Square Root ◽  
Root Extraction

The digital function filters – algorithms and applications

2013 ◽  
Vol 61 (2) ◽  
pp. 371-377
Author(s):  
M. Siwczyński ◽  
A. Drwal ◽  
S. Żaba
Keyword(s):  
Digital Filters ◽  
Phase Shifters ◽  
Square Root ◽  
Real Power ◽  
The Real ◽  
Distributed Parameters ◽  
Digital Modeling ◽  
Analysis And Synthesis ◽  
Basic Functions ◽  
Recursive Formulas

Abstract The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

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