Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing
For decades, geometric Brownian motion has proved a great success in describing the price process, because it catches the stochastic character of the price process. However, when it comes to commodity prices, there are several additional features. Mean reverting and jump diffusion phenomenon is two...
| Main Author: | |
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| Format: | Dissertation (University of Nottingham only) |
| Language: | English |
| Published: |
2015
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| Online Access: | https://eprints.nottingham.ac.uk/30047/ |
| _version_ | 1848793910094069760 |
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| author | Cao, Hang |
| author_facet | Cao, Hang |
| author_sort | Cao, Hang |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | For decades, geometric Brownian motion has proved a great success in describing the price process, because it catches the stochastic character of the price process. However, when it comes to commodity prices, there are several additional features. Mean reverting and jump diffusion phenomenon is two characters among them have been researched most in the past decades.
In this empirical dissertation, six different models for the mean reverting process and jump diffusion process are compared to assess whether the addition of these features will improve the original geometric Brownian motion model, where crude oil is chosen to study. This purpose is expected to be expected to be completed by two aspects of comparisons. The first comparison is in terms of spot price: the parameters of each model are estimated with in-sample data by maximum likelihood estimation, and then I compare the simulated prices of each model with actual prices by figure and statistics. The second comparison is about the option price: we estimate the parameters of the Monte Carlo method, and then compare the simulated option prices with the actual option price, where the best model is the model has the least difference.
The results of analysis suggest from spot price aspect, MRDJ (mean reverting model with double jumps) is the best fitted model; from option price aspect, GBMDJ (geometric Brownian motion with double jumps) is the most suitable model in short period, while MRDJ model is best fit model in long period. |
| first_indexed | 2025-11-14T19:07:48Z |
| format | Dissertation (University of Nottingham only) |
| id | nottingham-30047 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:07:48Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-300472017-10-19T14:58:54Z https://eprints.nottingham.ac.uk/30047/ Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing Cao, Hang For decades, geometric Brownian motion has proved a great success in describing the price process, because it catches the stochastic character of the price process. However, when it comes to commodity prices, there are several additional features. Mean reverting and jump diffusion phenomenon is two characters among them have been researched most in the past decades. In this empirical dissertation, six different models for the mean reverting process and jump diffusion process are compared to assess whether the addition of these features will improve the original geometric Brownian motion model, where crude oil is chosen to study. This purpose is expected to be expected to be completed by two aspects of comparisons. The first comparison is in terms of spot price: the parameters of each model are estimated with in-sample data by maximum likelihood estimation, and then I compare the simulated prices of each model with actual prices by figure and statistics. The second comparison is about the option price: we estimate the parameters of the Monte Carlo method, and then compare the simulated option prices with the actual option price, where the best model is the model has the least difference. The results of analysis suggest from spot price aspect, MRDJ (mean reverting model with double jumps) is the best fitted model; from option price aspect, GBMDJ (geometric Brownian motion with double jumps) is the most suitable model in short period, while MRDJ model is best fit model in long period. 2015-09-16 Dissertation (University of Nottingham only) NonPeerReviewed application/pdf en https://eprints.nottingham.ac.uk/30047/1/dissertation.pdf Cao, Hang (2015) Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing. [Dissertation (University of Nottingham only)] |
| spellingShingle | Cao, Hang Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing |
| title | Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing |
| title_full | Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing |
| title_fullStr | Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing |
| title_full_unstemmed | Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing |
| title_short | Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing |
| title_sort | stochastic models of crude oil prices and their applications on option pricing |
| url | https://eprints.nottingham.ac.uk/30047/ |