scholarly journals Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Fakharany ◽  
R. Company ◽  
L. Jódar
Keyword(s):  
Option Pricing ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Stable Process ◽  
Integration Formula ◽  
Pricing Models ◽  
Integral Term ◽  
Pricing Problems ◽  
Stability And Consistency ◽  
Partial Integrodifferential Equation

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included.

scholarly journals Positive Solutions of European Option Pricing with CGMY Process Models Using Double Discretization Difference Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
R. Company ◽  
L. Jódar ◽  
M. Fakharany
Keyword(s):  
Option Pricing ◽  
Explicit Scheme ◽  
Process Models ◽  
European Option ◽  
Pricing Models ◽  
European Option Pricing ◽  
Change Of Variables ◽  
Discretization Schemes ◽  
Suitable Change ◽  
Stability And Consistency

This paper deals with the numerical analysis of PIDE option pricing models with CGMY process using double discretization schemes. This approach assumes weaker hypotheses of the solution on the numerical boundary domain than other relevant papers. Positivity, stability, and consistency are studied. An explicit scheme is proposed after a suitable change of variables. Advantages of the proposed schemes are illustrated with appropriate examples.

Efficient conservative second-order central-upwind schemes for option-pricing problems

2019 ◽  
Vol 22 (5) ◽  
pp. 71-101 ◽  
Author(s):  
Omishwary Bhatoo ◽  
Arshad Ahmud Iqbal Peer ◽  
Eitan Tadmor ◽  
Desire Yannick Tangman ◽  
Aslam Aly El Faidal Saib
Keyword(s):  
Option Pricing ◽  
Second Order ◽  
Upwind Schemes ◽  
Pricing Problems

Joint Calibration of Option Pricing Models via Particle Methods

2005 ◽  
Author(s):  
Billy Amzal ◽  
Yonathan Ebguy ◽  
Sebastien Roland
Keyword(s):  
Option Pricing ◽  
Particle Methods ◽  
Pricing Models

scholarly journals A fractional order epidemic model for the simulation of outbreaks of Ebola

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali
Keyword(s):  
Numerical Solution ◽  
Root Mean Square ◽  
Fractional Order ◽  
Relative Error ◽  
Numerical Solutions ◽  
Real Data ◽  
Mean Square ◽  
Order Model ◽  
The Real ◽  
Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

Sign in / Sign up

Export Citation Format

Share Document