Evaluation of Perpetual American Put Options with General Payoff
In this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms of elasticity. This form...
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MDPI AG
2025-06-01
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| Online Access: | https://www.mdpi.com/2227-9091/13/6/112 |
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| author | Luca Anzilli Lucianna Cananà |
| author_facet | Luca Anzilli Lucianna Cananà |
| author_sort | Luca Anzilli |
| collection | DOAJ |
| description | In this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms of elasticity. This formulation enables us to demonstrate that the considered pricing problem admits a unique solution when the payoff function exhibits strictly decreasing elasticity with respect to the underlying asset. Furthermore, this approach allows us to derive closed-form solutions for option pricing. |
| format | Article |
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| institution | Kabale University |
| issn | 2227-9091 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Risks |
| spelling | doaj-art-a5bee5e02f3e48249f5838475243a0fb2025-08-20T03:27:32ZengMDPI AGRisks2227-90912025-06-0113611210.3390/risks13060112Evaluation of Perpetual American Put Options with General PayoffLuca Anzilli0Lucianna Cananà1Department of Economic Sciences, University of Salento, 73100 Lecce, ItalyIonian Department of Law, Economics and Environment, University of Bari “Aldo Moro”, 74121 Taranto, ItalyIn this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms of elasticity. This formulation enables us to demonstrate that the considered pricing problem admits a unique solution when the payoff function exhibits strictly decreasing elasticity with respect to the underlying asset. Furthermore, this approach allows us to derive closed-form solutions for option pricing.https://www.mdpi.com/2227-9091/13/6/112perpetual American optionoption pricingnon-linear payofffree-boundary problemelasticitypower option |
| spellingShingle | Luca Anzilli Lucianna Cananà Evaluation of Perpetual American Put Options with General Payoff Risks perpetual American option option pricing non-linear payoff free-boundary problem elasticity power option |
| title | Evaluation of Perpetual American Put Options with General Payoff |
| title_full | Evaluation of Perpetual American Put Options with General Payoff |
| title_fullStr | Evaluation of Perpetual American Put Options with General Payoff |
| title_full_unstemmed | Evaluation of Perpetual American Put Options with General Payoff |
| title_short | Evaluation of Perpetual American Put Options with General Payoff |
| title_sort | evaluation of perpetual american put options with general payoff |
| topic | perpetual American option option pricing non-linear payoff free-boundary problem elasticity power option |
| url | https://www.mdpi.com/2227-9091/13/6/112 |
| work_keys_str_mv | AT lucaanzilli evaluationofperpetualamericanputoptionswithgeneralpayoff AT luciannacanana evaluationofperpetualamericanputoptionswithgeneralpayoff |