Modeling non-linearity in asset returns

The first essay develops a new conditional jump model to study jump dynamics in stock market returns. We propose a simple filter to infer ex post the distribution of jumps. This permits construction of the shock affecting the time t conditional jump intensity, and is the main input into an autoregressive conditional jump intensity model. The model allows the conditional jump intensity to be time-varying and follows an approximate ARMA form. Daily stock returns are analyzed using the jump model coupled with a GARCH specification of volatility. We find significant time-variation in the conditional jump intensity and evidence of time-variation in the jump size distribution. The conditional jump dynamics contribute to a good in-sample and out-of-sample fit to stock market volatility, and capture the rally often observed in equity markets following a significant downturn.; The second essay develops a new bivariate jump model to study jump dynamics in foreign exchange returns. The model extends a bivariate GARCH parameterization to include a correlated jump process. The conditional covariance matrix has the BEKK structure, while the bivariate jumps are governed by a Correlated Bivariate Poisson (CBP) function. Using daily data we find evidence of both independent currency-specific jumps and jumps common to both exchange rates. The essay concludes by investigating a time-varying structure for the arrival of jumps that relaxes the assumption of a constant and bounded jump correlation imposed by the CBP function.; The third essay extends the recent empirical literature on risk-adjusted Hotelling Rules for exhaustible resources by allowing time-varying risk premia in resource asset returns. Monthly metal prices for four metals (lead, copper, silver, and zinc) are used to estimate a Bivariate GARCH-M model derived from the risk-adjusted Hotelling rule and the consumption-based Intertemporal Asset Pricing Model (IAPM) of resource asset returns. The model is also augmented with the Correlated Bivariate Poisson jump component to study the effect of market crashes on resource returns. The results basically reject the hypothesis that a time-varying risk premium provide a key component in modeling nonrenewable resource asset returns.