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Abstract
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This work is concentrated on the microeconomic foundation of modern option pricing models. In this research I developed a model of market agents' interactions, induced by heterogeneity of information, which is consistent with both modern option pricing models and empirical facts about stock price behaviour -- the connection between volatility, number of trades and volume of trade is of particular interest.
Moreover, I resolved a long standing disagreement about the relative impact of number of trades and volume of trade on the volatility process, by showing that their role depends on the time scale on which the price process is considered. It follows from the model presented that on a large time scale (i.e. if the price process is sampled infrequently), the price process is a geometric Brownian Motion if the order processing cost is negligible.
On the other hand, if the order processing cost is small, but not zero then the price process is time changed geometric Brownian Motion with the time change given by the number of trades. The empirical test of the model developed in this work shows that, at very high frequency, the volume of trade is able to explain more then one third of the variability in asset returns.
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