This dissertation investigates the volatility of the relationships between exchange rates and interest rates. The first part of the paper explores the transmission relationship between these two markets using a time-series model. Previous studies have assumed that covariance was constant in both markets. However, if the volatilities of the exchange rate and interest rate markets are correlated over time, the interaction and spillover effects between the two markets may be affected by time-varying covariance. Hence, this paper utilizes the BEKK-GARCH model developed by Engle and Kroner (1995) to capture the dynamic relationship between the exchange rates and interest rates. This study uses the returns data for G7 members¡¦ exchange rates and interest rates to test whether these markets exhibited volatilities spillover from 1978 to 2009. The results show bi-directional volatility spillovers in the markets of the UK, the Euro countries, and Canada, where the volatilities of the two markets were interrelated. The second part of the paper explores the relationship between exchange rates and interest rates using a jump diffusion model. Previous studies assumed that the dynamic processes of exchange rates and interest rates follow a diffusion process with a continuous time path, but an increasing number of empirical studies have shown that a continuous diffusion stochastic model does not capture the dynamic process of these variables. Thus, this paper investigates the discontinuous variables of exchange rates and interest rates and assumes that these variables follow a jump diffusion process. The UIRP model is employed to explore the relationship between both variables and to divide the systematic risk into systematic continuous risk and systematic jump risk. The returns data for G7 members¡¦ exchange rates and interest rates from 2005 to 2010 were analyzed to test whether the expected exchange rate is affected by jump components when the interest rate market experiences a jump. The results show that the jump diffusion model has more explanatory power than the pure diffusion model does, and, when the interest rate market experiences a jump risk, the systematic jump risk has a significant relationship with the expected exchange rates in some G7 countries.

In this thesis the GARCH models are applied to evaluate financial options and futures. In the first application, the GARCH models in parsimonious form are studied for pricing the S&P500 options. Unlike previous studies that focus on developed formulation, the results indicate that simplified models provide effective performance and it is the simple GARCH model that yields the least valuation error. To our consideration, examining model possessing simplification is of practical importance because model estimation becomes readily accessible through available econometric software, which circumvent programming barriers in implementing alternative one’s own pricing methods. The second application consider the component GARCH models for currency option pricing. The valuation results favour the component formulations particularly in the pricing of long term contracts. Volatility modelling results indicate that the return-volatility relationship is symmetric in the long run, but over the short term asymmetry also arises in the EURUSD and GBPUSD exchange rates. The third application evaluates canola futures in Canada in relation to spot market price. Results confirm the cointegrating relationship with threshold corresponding to transaction and adjustment cost. And it is the futures market that adjusts actively to price disparities but in the meantime there is volatility spillover from futures to the spot market. Overall, our empirical assessments indicate the importance of the time varying volatility and the improvements achieved in option pricing and futures evaluation. We believe the present study’s analysis provides useful suggestions and further guidance to practitioners and investors for the pricing and trading in the equity and foreign exchange markets, also to the market agents to better evaluate price uncertainty in order to guard against adverse price changes.