# Financial Volatility and Time-Varying Risk Premia

Abstract: This thesis consists of four empirical essays, all dealing with return volatility of financial assets and/or time-varying risk premia. In the first essay, Changing Risk Premia: Evidence from a Small Open Economy, the relation between risk and return is investigated for Swedish stocks. Little is known about the differences in the risk-return relationship in large economies compared with smaller, less studied, markets. In the paper, Sweden is used as a representative for small open economies. The price of risk on the Swedish stock market is estimated using a conditional asset pricing model that allows for time-variation in the risk. The results of the econometric analysis show that the estimates of the price of risk are invariably positive and significant, and that there are only minor differences in the preferences towards risk of representative investors in small and large economies. The second essay, Time-Varying Risk Premia in Swedish Treasury Bonds, models time-varying risk premia at the long end of the Swedish term structure using a GARCH-M approach. Two measures of risk are used to model the premia; the conditional variance of the excess holding return, and the conditional covariance with the market portfolio return. The results show that there is evidence of time-varying risk premia of a conditional CAPM type in excess holding period returns of Swedish treasury bonds. Furthermore, it is found that the estimated premia can be of substantial magnitude during periods of great uncertainty. In the third essay, Forecasting Variance Using Stochastic Volatility and GARCH, various GARCH and stochastic volatility specifications are compared with respect to their in-sample characteristics and their ability to accurately predict volatility, using daily Swedish OMX-index returns. The analysis shows that the stochastic volatility models are superior to the GARCH/EGARCH models in their ability to capture the features of the data, and that the asymmetric and seasonal effects are important. The forecasting ability of the models is evaluated using a bootstrap technique for forecast horizons between 2 and 100 days. The main result is that the stochastic volatility models produce significantly more accurate volatility forecasts than the GARCH/EGARCH models, but that there are only minor differences between the various stochastic volatility specifications. The fourth essay, Stochastic Volatility and the Estimation of Short Term Interest Rate Dynamics, estimates a two-factor stochastic volatility model for the default-free short-term interest rate, using Euro-market data for eight different currencies. The results show that there is a highly persistent stochastic volatility component present in the short-term interest rate which is captured by the model. In addition, there is evidence of a level effect in the volatility of the short rate, i.e. that the volatility of the short term interest rate depends on the level of the short rate itself. The two-factor model clearly outperforms a model that only allows for a level effect, in terms of its ability to capture the features of the data. Furthermore, the two-factor model gives theoretical call option values that can differ substantially from those obtained by other models. This is especially true for short-maturity out-of-the-money options.

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