The numerical method for solving the problem of pricing an American put-option

The paper presents a computational algorithm for solving the problem of pricing an American put-option described by the Black-Sholes equation. Firstly, two changes of variables are presented. First change is used to eliminate a discontinuity of solution derivatives. The second one transforms the equ...

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Bibliographic Details
Main Authors: Gileva, L., Shaydurov, V., Efremov, A.
Format: Conference Proceeding
Language:English
Subjects:
Algorithms
Boundary conditions
Domains
Finite difference method
Free boundaries
Iterative methods
Numerical methods
Pricing
Online Access:Get full text
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Summary:The paper presents a computational algorithm for solving the problem of pricing an American put-option described by the Black-Sholes equation. Firstly, two changes of variables are presented. First change is used to eliminate a discontinuity of solution derivatives. The second one transforms the equation on the domain with free boundary to the equation with an unknown coeffcient on a domain with fixed boundary. Secondly, the finite-difference approximation of the obtained equation is fulfilled including boundary condition at infinity. Finally, the computational algorithm is presented for solving discrete analogue of parabolic equation with iteration of the secant method at each time layer to found an unknown coeffcient with the help of the additional boundary condition.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0033522