UBC Theses and Dissertations

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UBC Theses and Dissertations

Essays on financial asset pricing Smith, Maxwell R.


The first essay of this thesis is concerned with the pricing of financial assets in positive net supply in a financial market with continuous time trading. A general equilibrium, continuous time model of an economy with production is developed. The model is used to develop a nonlinear partial differential equation whose solution gives the market price of the economy's aggregate long term physical/financial assets in terms of the consumption good. Partial differential equations that are linear are then developed for pricing individual physical/financial asset using the solution for the economy's aggregate of physical/financial assets. A particular solution is presented and applications to the pricing of bonds and the pricing of warrants and stock are made. Unlike previous models, financial assets represent a significant portion of the economy's wealth in this model. The model is generalized to include two kinds of production: risky instantaneous production of the consumption good and riskless production of long term physical/financial assets whose output is risky. The second essay develops the concept of market risk, which arises from the uncertainty investors have about the economy and the financial markets they trade in. A simple three date model with log and risk neutral investors trading a stock and bond is considered first. Market risk is modeled by introducing economy states which represent the possible economies that traders could be trading in. Two possible equilibria are shown to exist in the model: a separating equilibrium in which market prices reveal the economy state associated with the magnitude of the aggregate endowments of investors and a pooling equilibrium in which first period prices do not reveal the economy state. The concept of market risk, is used to develop a model of market crashes. Market crashes are modeled as pooling equilibria where the market price initially does not reveal the fundamental value of a financial asset and may not do so until the last trading opportunity takes place. The market price represents an average of possible final market prices. When the market price moves down sharply from a pooling price to a separating price that reveals the economy state the market crash takes place. The market crash occurs when a pooling price that does not reveal the economy state is no longer an equilibrium for the prevailing underlying economy state. Then the price must change and the economy state is revealed. Two methods of triggering the market crash are considered, one based upon information arriving to the market, the other based upon the arrival of new investors.

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