A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure Models
The primary objective of this paper is to expand Jamshidian’s bond option formula and compatible one-factor term structure models by incorporating the existence of uncertainty in the parameters governing interest-rate fluctuations. Specifically, we consider imprecision in the parameters related to t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/7/668 |
| _version_ | 1797590305652867072 |
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| author | Jorge de Andrés-Sánchez |
| author_facet | Jorge de Andrés-Sánchez |
| author_sort | Jorge de Andrés-Sánchez |
| collection | DOAJ |
| description | The primary objective of this paper is to expand Jamshidian’s bond option formula and compatible one-factor term structure models by incorporating the existence of uncertainty in the parameters governing interest-rate fluctuations. Specifically, we consider imprecision in the parameters related to the speed of reversion, equilibrium short-term interest rate, and volatility. To model this uncertainty, we utilize fuzzy numbers, which, in this context, are interpreted as epistemic fuzzy sets. The second objective of this study is to propose a methodology for estimating these parameters based on historical data. To do so, we use the possibility distribution functions capability to quantify imprecise probability distributions. Furthermore, this paper presents an application to the term structure of fixed-income bonds with the highest credit rating in the Euro area. This empirical application allows for evaluating the effectiveness of the fuzzy extension in fitting the dynamics of interest rates and assessing the suitability of the proposed extension. |
| first_indexed | 2024-03-11T01:18:42Z |
| format | Article |
| id | doaj.art-82e64e3d6aa6471582706ad830239cfd |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T01:18:42Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-82e64e3d6aa6471582706ad830239cfd2023-11-18T18:17:47ZengMDPI AGAxioms2075-16802023-07-0112766810.3390/axioms12070668A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure ModelsJorge de Andrés-Sánchez0Social and Business Research Laboratory, University Rovira i Virgili, Campus Bellissens, 43204 Reus, SpainThe primary objective of this paper is to expand Jamshidian’s bond option formula and compatible one-factor term structure models by incorporating the existence of uncertainty in the parameters governing interest-rate fluctuations. Specifically, we consider imprecision in the parameters related to the speed of reversion, equilibrium short-term interest rate, and volatility. To model this uncertainty, we utilize fuzzy numbers, which, in this context, are interpreted as epistemic fuzzy sets. The second objective of this study is to propose a methodology for estimating these parameters based on historical data. To do so, we use the possibility distribution functions capability to quantify imprecise probability distributions. Furthermore, this paper presents an application to the term structure of fixed-income bonds with the highest credit rating in the Euro area. This empirical application allows for evaluating the effectiveness of the fuzzy extension in fitting the dynamics of interest rates and assessing the suitability of the proposed extension.https://www.mdpi.com/2075-1680/12/7/668fuzzy-random variablesfuzzy numbersfuzzy-random option pricingprobability–possibility transformationVasicek’s model of term structureJamshidian’s bond option model |
| spellingShingle | Jorge de Andrés-Sánchez A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure Models Axioms fuzzy-random variables fuzzy numbers fuzzy-random option pricing probability–possibility transformation Vasicek’s model of term structure Jamshidian’s bond option model |
| title | A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure Models |
| title_full | A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure Models |
| title_fullStr | A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure Models |
| title_full_unstemmed | A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure Models |
| title_short | A Fuzzy-Random Extension of Jamshidian’s Bond Option Pricing Model and Compatible One-Factor Term Structure Models |
| title_sort | fuzzy random extension of jamshidian s bond option pricing model and compatible one factor term structure models |
| topic | fuzzy-random variables fuzzy numbers fuzzy-random option pricing probability–possibility transformation Vasicek’s model of term structure Jamshidian’s bond option model |
| url | https://www.mdpi.com/2075-1680/12/7/668 |
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