scholarly journals Finite Difference Method for the Hull–White Partial Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1719
Author(s):  
Yongwoong Lee ◽  
Kisung Yang
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Trading Volume ◽  
Operator Splitting ◽  
Splitting Method ◽  
Analytic Solutions ◽  
Partial Differential

This paper reviews the finite difference method (FDM) for pricing interest rate derivatives (IRDs) under the Hull–White Extended Vasicek model (HW model) and provides the MATLAB codes for it. Among the financial derivatives on various underlying assets, IRDs have the largest trading volume and the HW model is widely used for pricing them. We introduce general backgrounds of the HW model, its associated partial differential equations (PDEs), and FDM formulation for one- and two-asset problems. The two-asset problem is solved by the basic operator splitting method. For numerical tests, one- and two-asset bond options are considered. The computational results show close values to analytic solutions. We conclude with a brief comment on the research topics for the PDE approach to IRD pricing.

scholarly journals CMMSE: A technique for generating adapted discretizations to solve partial differential equations with the generalized finite difference method

2021 ◽  
Author(s):  
Augusto César Ferreira ◽  
Miguel Ureña ◽  
HIGINIO RAMOS
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Meshless Method ◽  
Computational Cost ◽  
Partial Differential

The generalized finite difference method is a meshless method for solving partial differential equations that allows arbitrary discretizations of points. Typically, the discretizations have the same density of points in the domain. We propose a technique to get adapted discretizations for the solution of partial differential equations. This strategy allows using a smaller number of points and a lower computational cost to achieve the same accuracy that would be obtained with a regular discretization.

scholarly journals Modelling the Flow of Mass and Energy within a Snowpack for Hydrological Forecasting

1983 ◽  
Vol 4 ◽  
pp. 198-203 ◽  
Author(s):  
E. M. Morris
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Snow Melt ◽  
Partial Differential ◽  
Hydrological Forecasting ◽  
Using Data

This paper describes a deterministic, distributed snow-melt model which has been developed for the Systeme Hydrologique Européen (SHE), The model is based on partial differential equations describing the flow of mass and energy through the snow. These equations are solved by an implicit, iterative finite-difference method. The behaviour of the model is investigated using data from a sub-Arctic site in Scotland.

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