An ETD Method for Vulnerable American Options
This paper introduces the exponential time differencing (ETD) technique as a numerical method to efficiently solve vulnerable American options pricing. We address several challenges, including removing cross-derivative terms through appropriate transformations, treating early-exercise opportunities...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-02-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/4/602 |
| _version_ | 1797297538119761920 |
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| author | Rafael Company Vera N. Egorova Lucas Jódar |
| author_facet | Rafael Company Vera N. Egorova Lucas Jódar |
| author_sort | Rafael Company |
| collection | DOAJ |
| description | This paper introduces the exponential time differencing (ETD) technique as a numerical method to efficiently solve vulnerable American options pricing. We address several challenges, including removing cross-derivative terms through appropriate transformations, treating early-exercise opportunities using the penalty method, and substituting fixed boundary conditions with corresponding one-sided finite differences. The proposed method is shown to be both accurate and efficient through numerical experiments, which also compare the results with existing methods and analyze the numerical stability and convergence rate. |
| first_indexed | 2024-03-07T22:22:46Z |
| format | Article |
| id | doaj.art-5475fc1f10eb4bc6a8b28804dedcef35 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-07T22:22:46Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5475fc1f10eb4bc6a8b28804dedcef352024-02-23T15:26:15ZengMDPI AGMathematics2227-73902024-02-0112460210.3390/math12040602An ETD Method for Vulnerable American OptionsRafael Company0Vera N. Egorova1Lucas Jódar2Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainDepartamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Avenida de los Castros, s/n, 39005 Santander, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainThis paper introduces the exponential time differencing (ETD) technique as a numerical method to efficiently solve vulnerable American options pricing. We address several challenges, including removing cross-derivative terms through appropriate transformations, treating early-exercise opportunities using the penalty method, and substituting fixed boundary conditions with corresponding one-sided finite differences. The proposed method is shown to be both accurate and efficient through numerical experiments, which also compare the results with existing methods and analyze the numerical stability and convergence rate.https://www.mdpi.com/2227-7390/12/4/602vulnerable optionsdefault riskexponential time differencingpenalty method |
| spellingShingle | Rafael Company Vera N. Egorova Lucas Jódar An ETD Method for Vulnerable American Options Mathematics vulnerable options default risk exponential time differencing penalty method |
| title | An ETD Method for Vulnerable American Options |
| title_full | An ETD Method for Vulnerable American Options |
| title_fullStr | An ETD Method for Vulnerable American Options |
| title_full_unstemmed | An ETD Method for Vulnerable American Options |
| title_short | An ETD Method for Vulnerable American Options |
| title_sort | etd method for vulnerable american options |
| topic | vulnerable options default risk exponential time differencing penalty method |
| url | https://www.mdpi.com/2227-7390/12/4/602 |
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