A Fast and Accurate Numerical Approach for Pricing American-Style Power Options
In this paper, we present a fast and accurate numerical approach applied to specific American-style derivatives, namely American power call and put options, whose main feature is that the underlying asset is raised to a power. The study is set in the Black–Scholes framework, and we consider continuo...
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MDPI AG
2025-06-01
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| Series: | Mathematics |
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| author | Tsvetelin S. Zaevski Hristo Sariev Mladen Savov |
| author_facet | Tsvetelin S. Zaevski Hristo Sariev Mladen Savov |
| author_sort | Tsvetelin S. Zaevski |
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| description | In this paper, we present a fast and accurate numerical approach applied to specific American-style derivatives, namely American power call and put options, whose main feature is that the underlying asset is raised to a power. The study is set in the Black–Scholes framework, and we consider continuously paying dividends assets and arbitrary positive values for the power. It is important to note that although a log-normal process raised to a power is again log-normal, the resulting change in variables may lead to a negative dividend rate, and this case remains largely understudied in the literature. We derive closed-form formulas for the perpetual options’ optimal boundaries and for the fair prices. For finite maturities, we approximate the optimal boundary using some first-hitting properties of the Brownian motion. As a consequence, we obtain the option price quickly and with relatively high accuracy—the error is at the third decimal position. We further provide a comprehensive analysis of the impact of the parameters on the options’ value, and discuss ordinary European and American capped options. Various numerical examples are provided. |
| format | Article |
| id | doaj-art-c7b02927350c42fb8d7ecee97fc0664c |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-c7b02927350c42fb8d7ecee97fc0664c2025-08-20T03:27:18ZengMDPI AGMathematics2227-73902025-06-011312203110.3390/math13122031A Fast and Accurate Numerical Approach for Pricing American-Style Power OptionsTsvetelin S. Zaevski0Hristo Sariev1Mladen Savov2Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, BulgariaIn this paper, we present a fast and accurate numerical approach applied to specific American-style derivatives, namely American power call and put options, whose main feature is that the underlying asset is raised to a power. The study is set in the Black–Scholes framework, and we consider continuously paying dividends assets and arbitrary positive values for the power. It is important to note that although a log-normal process raised to a power is again log-normal, the resulting change in variables may lead to a negative dividend rate, and this case remains largely understudied in the literature. We derive closed-form formulas for the perpetual options’ optimal boundaries and for the fair prices. For finite maturities, we approximate the optimal boundary using some first-hitting properties of the Brownian motion. As a consequence, we obtain the option price quickly and with relatively high accuracy—the error is at the third decimal position. We further provide a comprehensive analysis of the impact of the parameters on the options’ value, and discuss ordinary European and American capped options. Various numerical examples are provided.https://www.mdpi.com/2227-7390/13/12/2031American power optionsoptimal boundariesperpetual optionsfinite maturity optionscapped options |
| spellingShingle | Tsvetelin S. Zaevski Hristo Sariev Mladen Savov A Fast and Accurate Numerical Approach for Pricing American-Style Power Options Mathematics American power options optimal boundaries perpetual options finite maturity options capped options |
| title | A Fast and Accurate Numerical Approach for Pricing American-Style Power Options |
| title_full | A Fast and Accurate Numerical Approach for Pricing American-Style Power Options |
| title_fullStr | A Fast and Accurate Numerical Approach for Pricing American-Style Power Options |
| title_full_unstemmed | A Fast and Accurate Numerical Approach for Pricing American-Style Power Options |
| title_short | A Fast and Accurate Numerical Approach for Pricing American-Style Power Options |
| title_sort | fast and accurate numerical approach for pricing american style power options |
| topic | American power options optimal boundaries perpetual options finite maturity options capped options |
| url | https://www.mdpi.com/2227-7390/13/12/2031 |
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