Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917797314953216 |
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| author | Gnawali, Jagdish Lindquist, W. Brent Rachev, Svetlozar T. |
| author_facet | Gnawali, Jagdish Lindquist, W. Brent Rachev, Svetlozar T. |
| contents | We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets consist of a stock and a perpetual derivative of that stock. The option has the stock and its derivative as its underlying. Using a replicating portfolio, we develop prices for European options and generate the unique relationships between the risk-neutral and real-world parameters of the model. We discuss calibration of the model to empirical data in the cases in which the risky asset returns are treated as either arithmetic or logarithmic. From historical price and call option data for select large cap stocks, we develop implied parameter surfaces for the real-world parameters in the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis Gnawali, Jagdish Lindquist, W. Brent Rachev, Svetlozar T. Mathematical Finance Pricing of Securities We introduce a fairly general, recombining trinomial tree model in the natural world. Market-completeness is ensured by considering a market consisting of two risky assets, a riskless asset, and a European option. The two risky assets consist of a stock and a perpetual derivative of that stock. The option has the stock and its derivative as its underlying. Using a replicating portfolio, we develop prices for European options and generate the unique relationships between the risk-neutral and real-world parameters of the model. We discuss calibration of the model to empirical data in the cases in which the risky asset returns are treated as either arithmetic or logarithmic. From historical price and call option data for select large cap stocks, we develop implied parameter surfaces for the real-world parameters in the model. |
| title | Hedging via Perpetual Derivatives: Trinomial Option Pricing and Implied Parameter Surface Analysis |
| topic | Mathematical Finance Pricing of Securities |
| url | https://arxiv.org/abs/2410.04748 |