Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function
This paper proposes a framework based on the celebrated transform of Mellin type (MT) for the direct solution of the Black-Scholes-Merton European Put Option Model (BSMEPOM) on Dividend Yield (DY) with Modified-Log Payoff Function (MLPF) under the geometric Brownian motion. The focal goal of this pa...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Etamaths Publishing
2022-10-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/2638 |
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| author | S.E. Fadugba A.A. Adeniji M.C. Kekana J.T. Okunlola O. Faweya |
| author_facet | S.E. Fadugba A.A. Adeniji M.C. Kekana J.T. Okunlola O. Faweya |
| author_sort | S.E. Fadugba |
| collection | DOAJ |
| description | This paper proposes a framework based on the celebrated transform of Mellin type (MT) for the direct solution of the Black-Scholes-Merton European Put Option Model (BSMEPOM) on Dividend Yield (DY) with Modified-Log Payoff Function (MLPF) under the geometric Brownian motion. The focal goal of this paper is to use MT to obtain a valuation formula for the European Put Option (EPO) which pays a DY with MLPF. By means of the MT and its inversion formula, the price of EPO on DY was expressed in terms of integral equation. The valuation formula of EPO was obtained with the help of the convolution property of MT and final time condition. MT was tested on an illustrative example in order to measure its performance, effectiveness and suitability. The MLPF was compared with other existing payoff functions. Hence, the effect of DY on the pricing of EPO with MLPF was also investigated. |
| first_indexed | 2024-04-11T06:01:30Z |
| format | Article |
| id | doaj.art-fc13c9a9eb984f49979d3be1e70d880e |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-04-11T06:01:30Z |
| publishDate | 2022-10-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-fc13c9a9eb984f49979d3be1e70d880e2022-12-22T04:41:40ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392022-10-0120545410.28924/2291-8639-20-2022-542023Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff FunctionS.E. FadugbaA.A. AdenijiM.C. KekanaJ.T. OkunlolaO. FaweyaThis paper proposes a framework based on the celebrated transform of Mellin type (MT) for the direct solution of the Black-Scholes-Merton European Put Option Model (BSMEPOM) on Dividend Yield (DY) with Modified-Log Payoff Function (MLPF) under the geometric Brownian motion. The focal goal of this paper is to use MT to obtain a valuation formula for the European Put Option (EPO) which pays a DY with MLPF. By means of the MT and its inversion formula, the price of EPO on DY was expressed in terms of integral equation. The valuation formula of EPO was obtained with the help of the convolution property of MT and final time condition. MT was tested on an illustrative example in order to measure its performance, effectiveness and suitability. The MLPF was compared with other existing payoff functions. Hence, the effect of DY on the pricing of EPO with MLPF was also investigated.http://etamaths.com/index.php/ijaa/article/view/2638 |
| spellingShingle | S.E. Fadugba A.A. Adeniji M.C. Kekana J.T. Okunlola O. Faweya Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function International Journal of Analysis and Applications |
| title | Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function |
| title_full | Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function |
| title_fullStr | Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function |
| title_full_unstemmed | Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function |
| title_short | Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function |
| title_sort | direct solution of black scholes merton european put option model on dividend yield with modified log payoff function |
| url | http://etamaths.com/index.php/ijaa/article/view/2638 |
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