Three essays in financial econometrics

In this dissertation I explore, analyze and present new techniques in three areas of financial econometrics. In the first Chapter, I look at the risk premium in foreign exchange markets. The time varying risk premium is explored in a monetary economy in which the representative consumer is faced with the choice of tradable and nontradable consumption. For empirical testing, I do a detailed analysis of separating U.S. consumption data into tradable and non-tradable consumption. This separation provides us with a more accurate analysis of the model. In addition, I use the return on the currency futures contract to calculate the total return of investment in foreign currencies. Although this separation could account for some variability in the risk premium, it fails to produce sufficiently volatile risk premium which is inherent in the data. In Chapter 2, I model the time varying volatility of financial time series using option prices. I use a Kalman filter framework, for modelling and estimating the future variance using the term structure of the implied variance. I construct models for the relationship between the implied variances of options with different maturities and the expected next period variance and the option implied variance. I showed that these methods provide us with a better forecast of the next period variance and the future term structure of the implied volatility, compared with the four state Markov switching model and GARCH(1,1). In Chapter 3, I examine the stochastic volatility model using the daily range which is the difference between the maximum and the minimum of intraday prices. This method is more advantageous than using the daily return or the extreme values by themselves. I show the logarithm of the range and some other functions of the range are very dose to a normally distributed variable. The range is a more efficient and a simpler technique of estimation of the parameters of the model and the underlying latent daily volatility compared with the daily returns, or even higher than daily frequency returns