Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.

A contribution towards the performance and structural understanding of copper and nickel salts as ammonia stores

The ongoing depletion of fossil fuels and the severe consequences of the greenhouse effect make the development of alternative energy systems crucially important. While hydrogen is, in principle, a promising alternative, releasing nothing but energy and pure water. Hydrogen storage is complicated and no completely viable technique has been proposed so far. This work is concerned with the study of one potential alternative to pure hydrogen: ammonia, and more specifically its storage in solids. Ammonia, NH3, can be regarded as a chemical hydrogen carrier with the advantages of strongly reduced flammability and explosiveness as compared to hydrogen. Furthermore, ammine metal salts presented here as promising ammonia stores easily store up to 50 wt.-% ammonia, giving them a volumetric energy density comparable to natural gas. The model system NiX2–NH3 ( X = Cl, Br, I) is studied thoroughly with respect to ammine salt formation, thermal decomposition, air stability and structural effects. The system CuX2–NH3 ( X = Cl, Br) has an adverse thermal decomposition behaviour, making it impractical for use as an ammonia store. This system is, however, most interesting from a structural point of view and some work concerning the study of the structural behaviour of this system is presented. Finally, close chemical relatives to the metal ammine halides, the metal ammine nitrates are studied. They exhibit interesting anion arrangements, which is an impressive showcase for the combination of diffraction and spectroscopic information. The characterisation techniques in this thesis range from powder diffraction over single crystal diffraction, spectroscopy, computational modelling, thermal analyses to gravimetric uptake experiments. Further highlights are the structure solutions and refinements from powder data of (NH4)2[NiCl4(H2O)(NH3)] and Ni(NH3)2(NO3)2, the combination of crystallographic and chemical information for the elucidation of the (NH4)2[NiCl4(H2O)(NH3)] formation reaction and the growth of single crystals under ammonia flow, a technique allowing the first documented successful growth and single crystal diffraction measurement for [Cu(NH3)6]Cl2.