The copula-based method in financial derivatives

Abstract

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 copula-based 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.