Lévy Interest Rate Models with a Long Memory
This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/10/1/2 |
| _version_ | 1797490616885575680 |
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| author | Donatien Hainaut |
| author_facet | Donatien Hainaut |
| author_sort | Donatien Hainaut |
| collection | DOAJ |
| description | This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier’s transform. |
| first_indexed | 2024-03-10T00:35:33Z |
| format | Article |
| id | doaj.art-9ab1d2c4112a4fd991857f0f3b3472c2 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-10T00:35:33Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-9ab1d2c4112a4fd991857f0f3b3472c22023-11-23T15:17:47ZengMDPI AGRisks2227-90912021-12-01101210.3390/risks10010002Lévy Interest Rate Models with a Long MemoryDonatien Hainaut0UCLouvain, LIDAM, Louvain-La-Neueve, 1348 Ottignies-Louvain-la-Neuve, BelgiumThis article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier’s transform.https://www.mdpi.com/2227-9091/10/1/2interest rateLévy processMittag–Leffler functionmean reverting process |
| spellingShingle | Donatien Hainaut Lévy Interest Rate Models with a Long Memory Risks interest rate Lévy process Mittag–Leffler function mean reverting process |
| title | Lévy Interest Rate Models with a Long Memory |
| title_full | Lévy Interest Rate Models with a Long Memory |
| title_fullStr | Lévy Interest Rate Models with a Long Memory |
| title_full_unstemmed | Lévy Interest Rate Models with a Long Memory |
| title_short | Lévy Interest Rate Models with a Long Memory |
| title_sort | levy interest rate models with a long memory |
| topic | interest rate Lévy process Mittag–Leffler function mean reverting process |
| url | https://www.mdpi.com/2227-9091/10/1/2 |
| work_keys_str_mv | AT donatienhainaut levyinterestratemodelswithalongmemory |