The copula-based method in financial derivatives

Dependence modelling plays an important role in portfolio construction, risk management, and derivatives pricing, and any inappropriate method could lead to suboptimal portfolios, inaccurate assessment of risk exposures, and biased pricing, respectively. Studies in the last decade have supported the superiority of a copula-based approach over the traditional linear correlation method of measuring dependence as it offers more flexibility than the latter does. Given the increasing importance of spread options in hedging and speculating on the future dependence between the underlying assets, this thesis focuses on copulabased spread option pricing and illustrates the two cases of Heating Oil-Crude Oil and Gasoline-Gasoline crack spreads. The copula approach allows the splitting of the joint distribution into a copula function and univariate marginal distributions. A commonly used approach to characterizing the marginal behaviour of asset returns assumes a time-varying conditional mean and volatility along with a constant distribution of mean zero and unit variance for the standardized residuals in the physical world. Then, a set of both constant and time-varying copula models is fitted to the data. Given that all parameters are estimated in the physical world, we utilize the generalized local risk-neutral valuation relationship to transform the dynamic system under the objective measure into that under the risk-neutral measure, and the option price can be computed using Monte Carlo simulation. In general, the chosen copula functions consistently generate option prices that are different from those under the benchmark constant Gaussian copula. The option prices computed from the Student's t copula are less than those from the Plackett copula across all strike price levels and with different univariate marginal distributions. The departure from the Gaussian assumption found in the marginal distributions and dependence structure provides further evidence for the non-normality of financial markets. Moreover, the widely used linear correlation method potentially biases multi-asset option pricing. Declaration relating to disposition of project thesis/dissertation 1 hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstracts International (this is applicable to doctoral theses only). ···················-~si~~L . lf~jtt{L . X. U . Witness . f. /t.O. l. ~ . Date The University recognises that there may be exceptional circumstances requiring restrictions on copying or conditions on use. Requests for restriction for a period of up to 2 years must be made in writing. Requests for a longer period of restriction may be considered in exceptional circumstances and require the approval of the Dean of Graduate Research. FOR OFFICE USE ONLY Date of completion of requirements for Award: THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS ORIGINALITY STATEMENT 'I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged. ' Signed . ·'· . t. {9. ··~· . D. ~ . Date . J.! z.o. ~. ~ .