Applications of Numerical Methods in Economics and Finance
This dissertation consists of three articles on the applications of numerical methods in economics and finance. The first article investigates the performance of various estimators in estimating the continuous time short-term interest rate models under the assumption that the higher moment dynamics of the short rate series misspecified. The Monte Carlo evidence suggests that volatility of a continuous time short-term interest rate model would be estimated with a serious bias if the higher moments of the series are misspecified. Furthermore, in the root mean square sense, computationally intensive simulation based estimators do not exhibit better finite sample performance than the conventional estimators. The second article presents a numerical analysis of optimal initial and maintenance margin setting for futures commission merchants (future brokers). The problem is analyzed in a profit maximization context using a Markov chain approach and it is shown that the uncertainty regarding the futures price process, the trader's attitude toward a negative margin account and the transaction costs associated with margin calls lead the futures brokers to set positive performance margins without the need of legal enforcements of the futures exchange. The third article estimates the intertemporal allocation parameters using a new structural estimation technique, Simulated Residual Estimation. A series of Monte Carlo experiments which involve solving and simulating a life cycle model under both interest rate and income uncertainty are performed. The intertemporal allocation parameters, the elasticity of intertemporal substitution and the discount rate repeatedly estimated using the exact Euler equation, the approximate (long-linearized) Euler equation and the Simulated Residual Estimation. The results of the experiments suggest that the Simulated Residual Estimation has superior finite sample properties in comparison to conventional GMM based estimators even under the circumstances in which consumption data is measured with error.