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Book Description
It is well known that the volatility of financial returns is subject to continuous and persistent changes. Accordingly， many theoretical models have been built up to accommodate for the presence of such a feature. In this book， the authors emphasize the use of the popular ARCH models in formulating， estimating and testing the continuous time stochastic volatility models favored in the theoretical literature. The primary motivation of this research project is the result that although ARCH processes are stochastic difference equations， they can be thought of as reasonable approximations to the solutions of stochastic differential equations as the sampling frequency gets higher and higher. In this book， the authors make use of simulation based econometric methods and show how to test whether the approximation and filtering results for ARCH models are indeed valid. The statistical methodology used rests on the indirect inference principle， and is applied to a new class of fully articulated continuous time equilibrium models for the determination of the term structure of interest rates with stochastic volatility. This book also covers other research areas that are generated by the presence of stochastic volatility， such as market incompleteness， or imperfect hedging strategies that are optimal according to certain criteria. It also discusses some of the techniques that are typically needed to master and use the various setups that are built up through the book， such as the numerical integration of partial differential equations that typically arise in finance， or the convergence of difference equations to stochastic differential equations. The book is suitable for graduate students and scholars in financial markets econometrics and financial economics， but last year undergraduates will also find parts of this book useful reading.