Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach

Risk is often the most concerning factor in financial transactions. Option Greeks provide valuable insights into the risks inherent in option trading and serve as tools for risk mitigation. Traditionally, scholars compute option Greeks through extensive calculations. This article introduces an alter...

Full description

Saved in:
Bibliographic Details
Main Authors: Stefan Zecevic, Mariano Rodrigo
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/3/479
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850068106501685248
author Stefan Zecevic
Mariano Rodrigo
author_facet Stefan Zecevic
Mariano Rodrigo
author_sort Stefan Zecevic
collection DOAJ
description Risk is often the most concerning factor in financial transactions. Option Greeks provide valuable insights into the risks inherent in option trading and serve as tools for risk mitigation. Traditionally, scholars compute option Greeks through extensive calculations. This article introduces an alternative method that bypasses conventional derivative computation using the Mellin transform and its properties. Specifically, we derive Greeks for perpetual American options with general payoffs, represented as piecewise linear functions, and examine higher-order risk metrics for practical implications. Examples are provided to illustrate the effectiveness of our approach, offering a novel perspective on calculating and interpreting option Greeks.
format Article
id doaj-art-b2bc15a659b84de59cbf3c4b66811da3
institution DOAJ
issn 2227-7390
language English
publishDate 2025-01-01
publisher MDPI AG
record_format Article
series Mathematics
spelling doaj-art-b2bc15a659b84de59cbf3c4b66811da32025-08-20T02:48:09ZengMDPI AGMathematics2227-73902025-01-0113347910.3390/math13030479Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform ApproachStefan Zecevic0Mariano Rodrigo1School of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, AustraliaSchool of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, AustraliaRisk is often the most concerning factor in financial transactions. Option Greeks provide valuable insights into the risks inherent in option trading and serve as tools for risk mitigation. Traditionally, scholars compute option Greeks through extensive calculations. This article introduces an alternative method that bypasses conventional derivative computation using the Mellin transform and its properties. Specifically, we derive Greeks for perpetual American options with general payoffs, represented as piecewise linear functions, and examine higher-order risk metrics for practical implications. Examples are provided to illustrate the effectiveness of our approach, offering a novel perspective on calculating and interpreting option Greeks.https://www.mdpi.com/2227-7390/13/3/479financial derivativesMellin transformperpetual American optionstrading strategyhedging
spellingShingle Stefan Zecevic
Mariano Rodrigo
Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach
Mathematics
financial derivatives
Mellin transform
perpetual American options
trading strategy
hedging
title Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach
title_full Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach
title_fullStr Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach
title_full_unstemmed Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach
title_short Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach
title_sort explicit formulas for hedging parameters of perpetual american options with general payoffs a mellin transform approach
topic financial derivatives
Mellin transform
perpetual American options
trading strategy
hedging
url https://www.mdpi.com/2227-7390/13/3/479
work_keys_str_mv AT stefanzecevic explicitformulasforhedgingparametersofperpetualamericanoptionswithgeneralpayoffsamellintransformapproach
AT marianorodrigo explicitformulasforhedgingparametersofperpetualamericanoptionswithgeneralpayoffsamellintransformapproach