Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing

Cao, Hang (2015) Stochastic Models of Crude Oil Prices and Their Applications on Option Pricing. [Dissertation (University of Nottingham only)]

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Abstract

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.

Item Type: Dissertation (University of Nottingham only)
Depositing User: CAO, Hang
Date Deposited: 23 Mar 2016 13:33
Last Modified: 01 Nov 2016 18:41
URI: http://eprints.nottingham.ac.uk/id/eprint/30047

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