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...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| 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 |