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The methodology for determining the value of a claim whose payoffs depend upon the stochastic prices of other assets is referred to as Contingent Claims Analysis (CCA). This methodology has now become an industry standard for valuation of financial assets such as options, warrants, bonds, convertibles, and a host of other financial derivative securities. In recent years, techniques of Contingent Claims Analysis (CCA) and stochastic control theory have also been used to value risky ventures characterized by significant operating flexibility. While the advantages of these methods over alternative valuation approaches have been well documented, implementation problems have emerged, primarily due to the immense mathematical and computational complexity inherent in these approaches. The objectives of this dissertation are twofold. The first part is concerned with development of new lattice based option pricing algorithms that account for multiple sources of uncertainty and provide computational advantages when compared to existing models. The second part of this thesis is concerned with development of arbitrage based models for valuing real claims. Specifically, by applying techniques of Contingent Claims Analysis (CCA), and stochastic control theo ry, these new lattice based option pricing algorithms will be generalized to provide a multinomial lattice framework for valuation of risky ventures. |
