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Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions
In this paper, we derive the Laplace transforms, i.e., expected values of the exponentials, of time integrals of a class of Extended Cox–Ingersoll–Ross (CIR) processes which are given as the product of a standard CIR process and a positive deterministic function. Assuming such a process for the shor...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer International Publishing
2023
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10209971/ http://dx.doi.org/10.1007/s10203-023-00401-5 |
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author | Palapies, Lars |
author_facet | Palapies, Lars |
author_sort | Palapies, Lars |
collection | PubMed |
description | In this paper, we derive the Laplace transforms, i.e., expected values of the exponentials, of time integrals of a class of Extended Cox–Ingersoll–Ross (CIR) processes which are given as the product of a standard CIR process and a positive deterministic function. Assuming such a process for the short-rate gives rise to an affine term structure model for which we can now provide the bond price formulas that had so far not been accessible by attempting to solve the usual Riccati equation. By conditioning the exponentiated time integral on the potential states of the integrated process at its endpoint, we obtain the building blocks to evaluate certain interest rate derivatives, namely Bermudan swaptions. This is achieved by an algorithm that determines the exercise decision at each state by comparing the available payoff with an explicit lower bound built from such conditional Laplace transforms, without resorting to estimation techniques such as American Monte Carlo. |
format | Online Article Text |
id | pubmed-10209971 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-102099712023-05-26 Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions Palapies, Lars Decisions Econ Finan Article In this paper, we derive the Laplace transforms, i.e., expected values of the exponentials, of time integrals of a class of Extended Cox–Ingersoll–Ross (CIR) processes which are given as the product of a standard CIR process and a positive deterministic function. Assuming such a process for the short-rate gives rise to an affine term structure model for which we can now provide the bond price formulas that had so far not been accessible by attempting to solve the usual Riccati equation. By conditioning the exponentiated time integral on the potential states of the integrated process at its endpoint, we obtain the building blocks to evaluate certain interest rate derivatives, namely Bermudan swaptions. This is achieved by an algorithm that determines the exercise decision at each state by comparing the available payoff with an explicit lower bound built from such conditional Laplace transforms, without resorting to estimation techniques such as American Monte Carlo. Springer International Publishing 2023-05-25 /pmc/articles/PMC10209971/ http://dx.doi.org/10.1007/s10203-023-00401-5 Text en © The Author(s), under exclusive licence to Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Palapies, Lars Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions |
title | Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions |
title_full | Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions |
title_fullStr | Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions |
title_full_unstemmed | Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions |
title_short | Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions |
title_sort | laplace transforms of stochastic integrals and the pricing of bermudan swaptions |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10209971/ http://dx.doi.org/10.1007/s10203-023-00401-5 |
work_keys_str_mv | AT palapieslars laplacetransformsofstochasticintegralsandthepricingofbermudanswaptions |