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

Conservative Third-Order Central-Upwind Schemes for Option Pricing Problems

2019 ◽  
Vol 47 (4) ◽  
pp. 813-833
Author(s):  
Omishwary Bhatoo ◽  
Arshad Ahmud Iqbal Peer ◽  
Eitan Tadmor ◽  
Désiré Yannick Tangman ◽  
Aslam Aly El Faidal Saib
Keyword(s):  
Option Pricing ◽  
Third Order ◽  
Upwind Schemes ◽  
Pricing Problems

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 A mixed derivative terms removing method in multi-asset option pricing problems

2016 ◽  
Vol 60 ◽  
pp. 108-114 ◽  
Author(s):  
R. Company ◽  
V.N. Egorova ◽  
L. Jódar ◽  
F. Soleymani
Keyword(s):  
Option Pricing ◽  
Mixed Derivative ◽  
Pricing Problems

scholarly journals CABARET FINITE‐DIFFERENCE SCHEMES FOR THE ONE‐DIMENSIONAL EULER EQUATIONS

2001 ◽  
Vol 6 (2) ◽  
pp. 210-220 ◽  
Author(s):  
V. M. Goloviznin ◽  
T. P. Hynes ◽  
S. A. Karabasov
Keyword(s):  
Time Derivative ◽  
Second Order ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Gas Flows ◽  
Time Layer ◽  
One Dimensional ◽  
Upwind Schemes ◽  
The One ◽  
Solution Accuracy

In the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one‐dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer to improve the solution accuracy. Taking the first order Roe scheme as the basis we develop a few higher (i.e. second within regions of smooth solutions) order accurate difference schemes. One of them (CABARET3) is formulated in a two‐time‐layer form, which makes it most simple and robust. Supersonic and subsonic shock‐tube tests are used to compare the new schemes with several well‐known second‐order TVD schemes. In particular, it is shown that CABARET3 is notably more accurate than the standard second‐order Roe scheme with MUSCL flux splitting.

Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

2011 ◽  
Vol 1 (1) ◽  
pp. 82-88
Author(s):  
Hong-Kui Pang ◽  
Ying-Ying Zhang ◽  
Xiao-Qing Jin
Keyword(s):  
Differential Equation ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Option Pricing ◽  
Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Superlinear Convergence Rate ◽  
Pricing Problems ◽  
Toeplitz Systems ◽  
Toeplitz System

AbstractWe consider a nonsymmetric Toeplitz system which arises in the discretization of a partial integro-differential equation in option pricing problems. The preconditioned conjugate gradient method with a tri-diagonal preconditioner is used to solve this system. Theoretical analysis shows that under certain conditions the tri-diagonal preconditioner leads to a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

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