Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds
Freight derivative prices have been modeled assuming that the spot freight follows a particular stochastic process in order to manage them, like freight futures, forwards and options. However, an explicit formula for pricing freight options is not known, not even for simple spot freight processes. T...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/620 |
| _version_ | 1797570441309585408 |
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| author | Lourdes Gómez-Valle Miguel Angel López-Marcos Julia Martínez-Rodríguez |
| author_facet | Lourdes Gómez-Valle Miguel Angel López-Marcos Julia Martínez-Rodríguez |
| author_sort | Lourdes Gómez-Valle |
| collection | DOAJ |
| description | Freight derivative prices have been modeled assuming that the spot freight follows a particular stochastic process in order to manage them, like freight futures, forwards and options. However, an explicit formula for pricing freight options is not known, not even for simple spot freight processes. This is partly due to the fact that there is no valuation equation for pricing freight options. In this paper, we deal with this problem from two independent points of view. On the one hand, we provide a novel theoretical framework for pricing these Asian-style options. In this way, we build a partial differential equation whose solution is the freight option price obtained from stochastic delay differential equations. On the other hand, we prove lower and upper bounds for those freight options which enables us to estimate the option price. In this work, we consider that the spot freight rate follows a general stochastic diffusion process without restrictions in the drift and volatility functions. Finally, using recent data from the Baltic Exchange, we compare the described bounds with the freight option prices. |
| first_indexed | 2024-03-10T20:24:39Z |
| format | Article |
| id | doaj.art-e61956205f134acda81803dc798b411f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:24:39Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e61956205f134acda81803dc798b411f2023-11-19T21:54:22ZengMDPI AGMathematics2227-73902020-04-018462010.3390/math8040620Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional BoundsLourdes Gómez-Valle0Miguel Angel López-Marcos1Julia Martínez-Rodríguez2Departamento de Economía Aplicada e IMUVA, Facultad de Ciencias Económicas y Empresariales, Universidad de Valladolid, 47011 Valladolid, SpainDepartamento de Matemática Aplicada e IMUVA, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, SpainDepartamento de Economía Aplicada e IMUVA, Facultad de Ciencias Económicas y Empresariales, Universidad de Valladolid, 47011 Valladolid, SpainFreight derivative prices have been modeled assuming that the spot freight follows a particular stochastic process in order to manage them, like freight futures, forwards and options. However, an explicit formula for pricing freight options is not known, not even for simple spot freight processes. This is partly due to the fact that there is no valuation equation for pricing freight options. In this paper, we deal with this problem from two independent points of view. On the one hand, we provide a novel theoretical framework for pricing these Asian-style options. In this way, we build a partial differential equation whose solution is the freight option price obtained from stochastic delay differential equations. On the other hand, we prove lower and upper bounds for those freight options which enables us to estimate the option price. In this work, we consider that the spot freight rate follows a general stochastic diffusion process without restrictions in the drift and volatility functions. Finally, using recent data from the Baltic Exchange, we compare the described bounds with the freight option prices.https://www.mdpi.com/2227-7390/8/4/620spot freight ratesfreight optionsstochastic diffusion processstochastic delay differential equationrisk-neutral measurearbitration arguments |
| spellingShingle | Lourdes Gómez-Valle Miguel Angel López-Marcos Julia Martínez-Rodríguez Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds Mathematics spot freight rates freight options stochastic diffusion process stochastic delay differential equation risk-neutral measure arbitration arguments |
| title | Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds |
| title_full | Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds |
| title_fullStr | Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds |
| title_full_unstemmed | Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds |
| title_short | Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds |
| title_sort | two new strategies for pricing freight options by means of a valuation pde and by functional bounds |
| topic | spot freight rates freight options stochastic diffusion process stochastic delay differential equation risk-neutral measure arbitration arguments |
| url | https://www.mdpi.com/2227-7390/8/4/620 |
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