The path integral method in interest rate models

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dc.citation.epage136
dc.citation.issue1
dc.citation.spage125
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorЯнішевський, В. С.
dc.contributor.authorНоджак, Л. С.
dc.contributor.authorYanishevskyi, V. S.
dc.contributor.authorNodzhak, L. S.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-10-03T09:31:44Z
dc.date.available2023-10-03T09:31:44Z
dc.date.created2021-03-01
dc.date.issued2021-03-01
dc.description.abstractРозглянуто метод функціонального інтегрування в стохастичних моделях Мертона та Васічека відсоткової ставки. Продемонстровано побудову функціональних інтегралів двома способами: перший — за мірою Вінера з підстановкою розв’язків стохастичних рівнянь для моделей; другий — перехід від міри Вінера до міри інтегрування пов’язаної зі стохастичними змінними рівнянь Мертона та Васічека. Розглянуто введення граничних умов у другому способі для усунення некоректних часових асимптотик класичних моделей Мертона та Васічека відсоткових ставок. На прикладі моделі Мертона з нульовим дрейфом розглянуто граничну умову Діріхлє. Отримано представлення функціональним інтегралом для часової структури відсоткової ставки. Наведено оцінку отриманих функціональних інтегралів, де показано, що часова асимптотика є обмеженою.
dc.description.abstractAn application of path integral method to Merton and Vasicek stochastic models of interest rate is considered. Two approaches to a path integral construction are shown. The first approach consists in using Wieners measure with the following substitution of solutions of stochastic equations into the models. The second approach is realised by using transformation from Wieners measure to the integral measure related to the stochastic variables of Merton and Vasicek equations. The introduction of boundary conditions is considered in the second approach in order to remove incorrect time asymptotes from the classic Merton and Vasicek models of interest rates. By the example of Merton model with zero drift, a Dirichlet boundary condition is considered. A path integral representation of term structure of interest rate is obtained. The estimate of the obtained path integrals is performed, where it is shown that the time asymptote is limited.
dc.format.extent125-136
dc.format.pages12
dc.identifier.citationYanishevskyi V. S. The path integral method in interest rate models / V. S. Yanishevskyi, L. S. Nodzhak // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 1. — P. 125–136.
dc.identifier.citationenYanishevskyi V. S. The path integral method in interest rate models / V. S. Yanishevskyi, L. S. Nodzhak // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 1. — P. 125–136.
dc.identifier.doidoi.org/10.23939/mmc2021.01.125
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60324
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (8), 2021
dc.relation.references[1] Yuh-Dauh Lyuu. Financial Engineering and Computation: Principles, Mathematics, and Algorithms. Cambridge University Press (2004).
dc.relation.references[2] Privault N. An elementary introduction to stochastic interest rate modeling. World Scientific Publishing Co. Pte. Ltd. (2012).
dc.relation.references[3] Georges P. The Vasicek and CIR models and the expectation hypothesis of the interest rate term structure. Working Paper, Department of Finance (2003).
dc.relation.references[4] Decaps M., De Scheppe A., Goovaerts M. Applications of delta–function perturbation to the pricing of derivative securities. Physica A. 342, 93–40, 677–692 (2004).
dc.relation.references[5] Yanishevsky V. S. Stochastic methods in modeling of financial processes. Economics and society. 15, 959–965 (2018), (in Ukrainian).
dc.relation.references[6] Yanishevsky V. S. Option price for Bachelier model with constraints. Market Infrastructure. 19, 593–598 (2018), (in Ukrainian).
dc.relation.references[7] Kleinert H. Path integrals in quantum mechanics, statistics, polymer physics and financial markets. World Scientific Publishing Co., Inc., River Edge (2004).
dc.relation.references[8] Chaichian M., Demichev A. Path integrals in physics. Stochastic processes and quantum mechanics. Taylor & Francis (2001).
dc.relation.references[9] Chaichian M., Demichev A. Path integrals in physics. QFT, statistical physics and modern applications. Taylor & Francis (2001).
dc.relation.references[10] Baaquie B. E. Quantum finance. Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge University Press, New York (2004).
dc.relation.references[11] Linetsky V. The Path Integral Approach to Financial Modeling and Options Pricing. Computational Economics. 11, 129–163 (1998).
dc.relation.references[12] Blazhyevskyi L. F., Yanishevsky V. S. The path integral representation kernel of evolution operator in Merton–Garman model. Condensed Matter Physics. 14 (2), 23001 (2011).
dc.relation.references[13] Goovaertsa M., De Schepper A., Decampsa M. Closed-form approximations for diffusion densities: a path integral approach. Journal of Computational and Applied Mathematics. 164–165, 337–364 (2004).
dc.relation.references[14] Gardiner C. W. Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences.Springer (2004).
dc.relation.references[15] Grosche C. δ-function perturbations and boundary problems by path integration. Annalen der Physik. 2 (6), 557–589 (1993).
dc.relation.references[16] Grosche C., Steiner F. Handbook of Feynman Path Integrals. Springer, Berlin, Heidelberg (1998).
dc.relation.referencesen[1] Yuh-Dauh Lyuu. Financial Engineering and Computation: Principles, Mathematics, and Algorithms. Cambridge University Press (2004).
dc.relation.referencesen[2] Privault N. An elementary introduction to stochastic interest rate modeling. World Scientific Publishing Co. Pte. Ltd. (2012).
dc.relation.referencesen[3] Georges P. The Vasicek and CIR models and the expectation hypothesis of the interest rate term structure. Working Paper, Department of Finance (2003).
dc.relation.referencesen[4] Decaps M., De Scheppe A., Goovaerts M. Applications of delta–function perturbation to the pricing of derivative securities. Physica A. 342, 93–40, 677–692 (2004).
dc.relation.referencesen[5] Yanishevsky V. S. Stochastic methods in modeling of financial processes. Economics and society. 15, 959–965 (2018), (in Ukrainian).
dc.relation.referencesen[6] Yanishevsky V. S. Option price for Bachelier model with constraints. Market Infrastructure. 19, 593–598 (2018), (in Ukrainian).
dc.relation.referencesen[7] Kleinert H. Path integrals in quantum mechanics, statistics, polymer physics and financial markets. World Scientific Publishing Co., Inc., River Edge (2004).
dc.relation.referencesen[8] Chaichian M., Demichev A. Path integrals in physics. Stochastic processes and quantum mechanics. Taylor & Francis (2001).
dc.relation.referencesen[9] Chaichian M., Demichev A. Path integrals in physics. QFT, statistical physics and modern applications. Taylor & Francis (2001).
dc.relation.referencesen[10] Baaquie B. E. Quantum finance. Path Integrals and Hamiltonians for Options and Interest Rates. Cambridge University Press, New York (2004).
dc.relation.referencesen[11] Linetsky V. The Path Integral Approach to Financial Modeling and Options Pricing. Computational Economics. 11, 129–163 (1998).
dc.relation.referencesen[12] Blazhyevskyi L. F., Yanishevsky V. S. The path integral representation kernel of evolution operator in Merton–Garman model. Condensed Matter Physics. 14 (2), 23001 (2011).
dc.relation.referencesen[13] Goovaertsa M., De Schepper A., Decampsa M. Closed-form approximations for diffusion densities: a path integral approach. Journal of Computational and Applied Mathematics. 164–165, 337–364 (2004).
dc.relation.referencesen[14] Gardiner C. W. Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences.Springer (2004).
dc.relation.referencesen[15] Grosche C. d-function perturbations and boundary problems by path integration. Annalen der Physik. 2 (6), 557–589 (1993).
dc.relation.referencesen[16] Grosche C., Steiner F. Handbook of Feynman Path Integrals. Springer, Berlin, Heidelberg (1998).
dc.rights.holder© Національний університет “Львівська політехніка”, 2021
dc.subjectвідсоткова ставка
dc.subjectстохастична модель
dc.subjectумовна ймовірність
dc.subjectфункціональний інтеграл
dc.subjectinterest rate model
dc.subjectstochastic model
dc.subjecttransition probability
dc.subjectpath integral
dc.titleThe path integral method in interest rate models
dc.title.alternativeМетод функціонального інтегрування в моделях відсоткових ставок
dc.typeArticle

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