| This thesis investigates basket options on heterogeneous underlying assets. Our main contribution consists in considering a basket option on intrinsically different assets with stochastic interest rates. In the same basket, we combine commodity prices with stochastic convenience yields, exchange rates, and zero-coupon bonds. We treat all the aspects related to basket options: modelization, pricing, parameters estimation and basket hedging. Our contribution can be very useful, especially for practitioners who use this kind of product for hedging.; The second chapter of this research is a literature review on empirical methods used to estimate commodity and HJM models parameters. We also discuss the different methods available in the literature to price basket options. In the third chapter of this thesis, we compare, empirically, the performance of the heterogeneous basket option to that of a portfolio of individual options. The results show that the basket strategy is less expensive and more efficient. We apply the maximum-likelihood method to estimate the different parameters of the theoretical basket model as well as the correlations between these variables. As in Duan (1994), we use the maximum-likelihood approach adapted to unobservable variables to estimate the temporal series of the convenience yield as well as its parameters. Monte Carlo studies are conducted to examine the performance of the maximum-likelihood estimator in finite samples of simulated data. The results show that all the parameters estimates are convergent. We also estimate the model's parameters using real data. We find that most of the estimates are statistically significant and highly different from zero.; The fourth chapter deals with basket option pricing. Indeed, pricing a basket option is not a trivial task because there is no explicit analytical expression available for the distribution of the weighted sum of multiple correlated assets. Several approaches have been proposed in the literature to price basket options such as Monte Carlo simulations, tree-based methods, partial differential equations and analytical approximations. The last approach is the most attractive for practitioners because it is less time consuming than the other methods. In this thesis, we propose to extend three different analytical approximations, available in the literature, to the heterogeneous basket option case with stochastic interest rates. The moment matching approximations we use in this chapter are: reciprocal gamma, lognormal and Johnson family distributions. We examine the performance of each approximation. Since there is no closed-form formula for basket options, we carry out a Monte Carlo simulation with quadratic resampling technique to generate the benchmark values. We compute the root mean-squared error to measure the overall accuracy for a whole set of options based on a random choice of parameters and maximum absolute error to gauge the worst possible case. Our results show that the lognormal and the Johnson distributions give the most accurate results. (Abstract shortened by UMI.)... |
