| In the first chapter of this dissertation, I use no-arbitrage arguments to characterize families of consistent variance curve models parameterized in terms of observed variance swap rates. Absence of latent variables makes maximum likelihood estimation straightforward and no-arbitrage restrictions lead to significant efficiency gains in the estimation of drift parameters when inference is based on observations of several variance derivatives. Empirical results suggest that linear mean-reverting one-factor models provide inaccurate representation of the stochastic volatility dynamics.;In Chapter 2, I study volatility dynamics and volatility risk premia under alternative stochastic volatility models. Using daily data on S&P 500 returns and variance swap rates I find that two-factor models, in which the additional factor represents the level to which the spot variance reverts, significantly improve the fit of the term structure of variance derivatives. One-factor models may lead to risk premia term structures that understate the impact of the current state of the economy at longer horizons. Moreover, term structures from two-factor models generate different patterns during quiet and turbulent market periods.;The third chapter, coauthored with Mark W. Watson, shows how the Bai-Ng estimator can be modified to consistently estimate the number of dynamic factors in a restricted dynamic factor model. The modification is straightforward: The standard Bai-Ng estimator is applied to residuals obtained by projecting the observed data onto lagged values of principal-components estimates of the static factors. |
