Mathematical treatment of commodity markets.
Published: 2004
Language: eng
Number of pages: 221
Description: We study some mathematical problems that arise in the analysis of commodity markets. In the first chapter, we present a factor-model for the term structure of futures prices aimed at providing flexibility on the drivers. This allows a better fitting of curve movements for example contango and backwardation. We study the estimation of the parameters of the model based on Kalman-filter techniques. On the other hand, the factors' processes are found based on the absence of arbitrage. We consider the pricing of derivative securities where the underlyings are the model factors. In the search for closed form solutions, we find the joint distribution of the extreme values and endpoints of correlated Brownian motions with drift, as a summation of Sturm-Liouville functions.The third chapter deals with the relations between commodity movements and default events. We study both structural (Merton 1974, Giesecke 2003) and reduced form (Jarrow and Turnbull 1995) models in the context of Schwartz 1998 model for commodity futures prices. Several defaultable TS curves are presented, e.g. defaultable forward price. The processes for these TS are found based on the absence of arbitrage. Several commodity derivatives are proposed. In particular, we deal with the pricing of vulnerable options and basket derivatives in the context of constant recovery (Klein 1996). For this valuation, we use convenient change of measures and the multivariate distribution found in chapter 1.In the second chapter, based on the similarities between bonds and commodity term structures (TS), we generalize bond models such as Duffie-Kan 1996, Ahn, Dittmar and Gallant 2002 and Brace, Gatarek and Musiela 1997, to the world of commodities. We consider two transformations of futures prices, the identity and logarithmic. Due to the known complexity of futures prices TS, we create and deduce non-arbitrage processes for new families of models for example: polynomial models, (n-powers of the factors), and models with multivariate drivers. We also propose the idea of explaining complex commodities term structures by using more simple term structures.
Notes: Adviser:  Luis Seco.

Thesis (Ph.D.)--University of Toronto, 2004.

Electronic version licensed for access by U. of T. users.

Source: Dissertation Abstracts International, Volume: 65-10, Section: B, page: 5178.