Undergraduate Honors Theses

Thesis Defended

Spring 2015

Document Type

Thesis

Type of Thesis

Departmental Honors

Department

Economics

First Advisor

Carlos Martins-Filho

Second Advisor

Martin Boileau

Third Advisor

Daniel Brown

Abstract

Typically, the prices of financial assets are studied over fixed-time intervals such as the case with monthly or daily returns. Modern technology now allows us to consider each transac- tion that occurred throughout a trading period and the particular instance in time at which it was placed. Statistical analysis of financial assets conducted at this level is referred to as high frequency econometrics. This microscopic view of the market allows us to observe an asset’s price formation process in continuous time. High frequency data is marked by a number of peculiarities that do not persist in discrete-time financial data, thus requiring a different econometric approach in order to preserve the vast amount of microstructure information embedded in the transaction data. In this paper, we construct and specify the joint probability distribution of price movements and trade arrivals as a compound Poisson process to build a theoretical framework to study the interplay of volatility and the timing of trades. We extend the price decomposition model proposed by Rydberg and Shephard (2003) by defining the magnitude of price change process to follow an adaptation of the autoregressive conditional multinomial–a finite state, VARMA model originally developed by Engle and Russell (2005). Furthermore, we define the trade arrival process to be a doubly-stochastic Poisson process (or Cox process) and propose estimating its random intensity through kernel density estimation.

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