A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing
Since the early 2000s, fuzzy mathematics has fostered a stream of research on the financial valuation of assets incorporating optionality. This paper makes two contributions to this field. First, it conducts a bibliographical analysis of contributions from fuzzy set theory to option pricing, focusin...
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2025-01-01
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| author | Jorge de Andrés-Sánchez |
| author_facet | Jorge de Andrés-Sánchez |
| author_sort | Jorge de Andrés-Sánchez |
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| description | Since the early 2000s, fuzzy mathematics has fostered a stream of research on the financial valuation of assets incorporating optionality. This paper makes two contributions to this field. First, it conducts a bibliographical analysis of contributions from fuzzy set theory to option pricing, focusing on fuzzy-random option pricing (FROP) and its applications in binomial and trinomial lattice approaches. Second, it extends the FROP to yield curve modeling within a binomial framework. The bibliographical analysis followed the PRISMA guidelines and was conducted via the SCOPUS and WoS databases. We present a structured review of papers on FROP in discrete time (FROPDT), identifying the principal papers and outlets. The findings reveal that this focus has been applied to price options on stocks, stock indices, and real options. However, the exploration of its application to the term structure of interest-sensitive interest rate assets is very rare. To address this gap, we develop a fuzzy-random extension of the Ho–Lee term structure model, applying it to the European interbank market and price caplet options. |
| format | Article |
| id | doaj-art-9f99b0cf9e0443cbbe0cf918ede9d307 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-9f99b0cf9e0443cbbe0cf918ede9d3072025-01-24T13:22:16ZengMDPI AGAxioms2075-16802025-01-011415210.3390/axioms14010052A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate PricingJorge de Andrés-Sánchez0Social and Business Research Lab, Universitat Rovira i Virgili, Campus de Bellissens, 43204 Reus, SpainSince the early 2000s, fuzzy mathematics has fostered a stream of research on the financial valuation of assets incorporating optionality. This paper makes two contributions to this field. First, it conducts a bibliographical analysis of contributions from fuzzy set theory to option pricing, focusing on fuzzy-random option pricing (FROP) and its applications in binomial and trinomial lattice approaches. Second, it extends the FROP to yield curve modeling within a binomial framework. The bibliographical analysis followed the PRISMA guidelines and was conducted via the SCOPUS and WoS databases. We present a structured review of papers on FROP in discrete time (FROPDT), identifying the principal papers and outlets. The findings reveal that this focus has been applied to price options on stocks, stock indices, and real options. However, the exploration of its application to the term structure of interest-sensitive interest rate assets is very rare. To address this gap, we develop a fuzzy-random extension of the Ho–Lee term structure model, applying it to the European interbank market and price caplet options.https://www.mdpi.com/2075-1680/14/1/52option pricingfuzzy numbersfuzzy-random variablesfuzzy-random option pricingfuzzy-random option pricing in discrete timefuzzy-binomial yield models |
| spellingShingle | Jorge de Andrés-Sánchez A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing Axioms option pricing fuzzy numbers fuzzy-random variables fuzzy-random option pricing fuzzy-random option pricing in discrete time fuzzy-binomial yield models |
| title | A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing |
| title_full | A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing |
| title_fullStr | A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing |
| title_full_unstemmed | A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing |
| title_short | A Systematic Overview of Fuzzy-Random Option Pricing in Discrete Time and Fuzzy-Random Binomial Extension Sensitive Interest Rate Pricing |
| title_sort | systematic overview of fuzzy random option pricing in discrete time and fuzzy random binomial extension sensitive interest rate pricing |
| topic | option pricing fuzzy numbers fuzzy-random variables fuzzy-random option pricing fuzzy-random option pricing in discrete time fuzzy-binomial yield models |
| url | https://www.mdpi.com/2075-1680/14/1/52 |
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