Cai, C, De Angelis, T and Palczewski, J orcid.org/0000-0003-0235-8746 (2021) Optimal hedging of a perpetual American put with a single trade. SIAM Journal on Financial Mathematics (SIFIN), 12 (2). pp. 823-866. ISSN 1945-497X
Abstract
It is well-known that using delta hedging to hedge financial options is not feasible in practice. Traders often rely on discrete-time hedging strategies based on fixed trading times or fixed trading prices (i.e., trades occur only if the underlying asset's price reaches some predetermined values). Motivated by this insight and with the aim of obtaining explicit solutions, we consider the seller of a perpetual American put option who can hedge her portfolio once until the underlying stock price leaves a certain range of values $(a,b)$. We determine optimal trading boundaries as functions of the initial stock holding, and an optimal hedging strategy for a bond/stock portfolio. Optimality here refers to the variance of the hedging error at the (random) time when the stock leaves the interval $(a,b)$. Our study leads to analytical expressions for both the optimal boundaries and the optimal stock holding, which can be evaluated numerically with no effort.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021, Society for Industrial and Applied Mathematics. This is an author produced version of an article published in SIAM Journal on Financial Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | optimal hedging, discrete-time hedging, American put option, optimal stopping, free boundary problems |
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: | 13 Aug 2021 14:58 |
Last Modified: | 18 Sep 2021 15:54 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/20M1325265 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:177065 |