Cai, C, De Angelis, T and Palczewski, J orcid.org/0000-0003-0235-8746 (2022) The American put with finite-time maturity and stochastic interest rate. Mathematical Finance, 32 (4). pp. 1170-1213. ISSN 0960-1627
Abstract
In this paper, we study pricing of American put options on a nondividend-paying stock in the Black and Scholes market with a stochastic interest rate and finite-time maturity. We prove that the option value is a C1 function of the initial time, interest rate, and stock price. By means of Itô calculus, we rigorously derive the option value's early exercise premium formula and the associated hedging portfolio. We prove the existence of an optimal exercise boundary splitting the state space into continuation and stopping region. The boundary has a parametrization as a jointly continuous function of time and stock price, and it is the unique solution to an integral equation, which we compute numerically. Our results hold for a large class of interest rate models including CIR and Vasicek models. We show a numerical study of the option price and the optimal exercise boundary for Vasicek model.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Authors. This is an open access article published under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | American put option, free boundary problems, integral equations, stochastic interest rate. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Jul 2022 14:40 |
Last Modified: | 25 Jun 2023 23:02 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1111/mafi.12361 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:188978 |