Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance
The classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes the theoretical prices of bonds to be lower than t...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/9926131 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850174038758916096 |
|---|---|
| author | Chao Yue Chuanhe Shen |
| author_facet | Chao Yue Chuanhe Shen |
| author_sort | Chao Yue |
| collection | DOAJ |
| description | The classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes the theoretical prices of bonds to be lower than the actual market prices in the financial market. In order to change this situation, considering that the price change of the underlying is regarded as a fractal transmission system, the fractal derivative is introduced into the bond-pricing equation. In order to solve the fractal bond-pricing equation, we first convert it into an equivalent equation by using a fractal two-scale transform. Only in this case can we start to study it by means of the Lie symmetry analysis method. Then the geometric vector fields, the symmetry reductions, and the exact solution to the equations are obtained. Furthermore, the dynamic behaviors of the fractal bond-pricing equation are discussed. The results show that the fractal dimension bond-pricing formula can better explain price changes in the capital market than the classical one. That is to say, the classical bond-pricing equation is only a special case of the fractal-bond pricing equation, which makes up for the defect that the theoretical bond price given by the classical bond-pricing equation is often lower than the actual market price. The results of this paper provide a basis for bond pricing in the financial market in order to seek a more appropriate and real price. |
| format | Article |
| id | doaj-art-c7171f20ef794c5e8d7afe6f5f037535 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c7171f20ef794c5e8d7afe6f5f0375352025-08-20T02:19:44ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/9926131Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical FinanceChao Yue0Chuanhe Shen1School of EconomicsSchool of EconomicsThe classical bond-pricing models, as important financial tools, show strong vitality in bond pricing. However, these models also expose their theoretical defects, which leads to inconsistencies with the actual observation results and usually causes the theoretical prices of bonds to be lower than the actual market prices in the financial market. In order to change this situation, considering that the price change of the underlying is regarded as a fractal transmission system, the fractal derivative is introduced into the bond-pricing equation. In order to solve the fractal bond-pricing equation, we first convert it into an equivalent equation by using a fractal two-scale transform. Only in this case can we start to study it by means of the Lie symmetry analysis method. Then the geometric vector fields, the symmetry reductions, and the exact solution to the equations are obtained. Furthermore, the dynamic behaviors of the fractal bond-pricing equation are discussed. The results show that the fractal dimension bond-pricing formula can better explain price changes in the capital market than the classical one. That is to say, the classical bond-pricing equation is only a special case of the fractal-bond pricing equation, which makes up for the defect that the theoretical bond price given by the classical bond-pricing equation is often lower than the actual market price. The results of this paper provide a basis for bond pricing in the financial market in order to seek a more appropriate and real price.http://dx.doi.org/10.1155/2024/9926131 |
| spellingShingle | Chao Yue Chuanhe Shen Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance Journal of Mathematics |
| title | Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance |
| title_full | Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance |
| title_fullStr | Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance |
| title_full_unstemmed | Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance |
| title_short | Lie Symmetry Analysis for the Fractal Bond-Pricing Model of Mathematical Finance |
| title_sort | lie symmetry analysis for the fractal bond pricing model of mathematical finance |
| url | http://dx.doi.org/10.1155/2024/9926131 |
| work_keys_str_mv | AT chaoyue liesymmetryanalysisforthefractalbondpricingmodelofmathematicalfinance AT chuanheshen liesymmetryanalysisforthefractalbondpricingmodelofmathematicalfinance |