A dynamic semiparametric pricing method is proposed for financial derivatives including European and American type options and convertible bonds. The proposed method is an iterative procedure which uses nonparametric regression to approximate derivative values and parametric asset models to derive the continuation values. Extension to higher dimensional option pricing is also developed, in which the dependence structure of financial time series is modeled by copula functions. In the simulation study, we valuate one dimensional American options, convertible bonds and multi-dimensional American geometric average options and max options. The considered one-dimensional underlying asset models include the Black-Scholes, jump-diffusion, and nonlinear asymmetric GARCH models and for multivariate case we study copula models such as the Gaussian, Clayton and Gumbel copulae. Convergence of the method is proved under continuity assumption on the transition densities of the underlying asset models. And the orders of the supnorm errors are derived. Both the theoretical findings and the simulation results show the proposed approach to be tractable for numerical implementation and provides a unified and accurate technique for financial derivative pricing. The second part of this thesis studies the option pricing and hedging problems for conditional leptokurtic returns which is an important feature in financial data. The risk-neutral models for log and simple return models with heavy-tailed innovations are derived by an extended Girsanov change of measure, respectively. The result is applicable to the option pricing of the GARCH model with t innovations (GARCH-t) for simple eturn series. The dynamic semiparametric approach is extended to compute the option prices of conditional leptokurtic returns. The hedging strategy consistent with the extended Girsanov change of measure is constructed and is shown to have smaller cost variation than the commonly used delta hedging under the risk neutral measure. Simulation studies are also performed to show the effect of using GARCH-normal models to compute the option prices and delta hedging of GARCH-t model for plain vanilla and exotic options. The results indicate that there are little pricing and hedging differences between the normal and t innovations for plain vanilla and Asian options, yet significant disparities arise for barrier and lookback options due to improper distribution setting of the GARCH innovations.

The purpose of a cost model is to provide designers and decision-makers with accurate cost information to assess and compare multiple alternatives for obtaining the optimal solution and controlling cost. The cost models developed in the design phases are the most important and the most difficult to develop. Therefore it is necessary to identify appropriate cost drivers and employ appropriate modeling techniques to accurately estimate cost for directing designers. The objective of this study is to provide higher predictive accuracy of cost estimation for directing designer in the early design phases of complex products. After a generic cost estimation model is presented and the existing methods for identification of cost drivers and different cost modeling techniques are reviewed, the dissertation first proposes new methodologies to identify and select the cost drivers: Causal-Associated (CA) method and Tabu-Stepwise selection approach. The CA method increases understanding and explanation of the cost analysis and helps avoid missing some cost drivers. The Tabu-Stepwise selection approach is used to select significant cost drivers and eliminate irrelevant cost drivers under nonlinear situation. A case study is created to illustrate their procedure and benefits. The test data show they can improve predictive capacity. Second, this dissertation introduces Tabu-SVR, a nonparametric approach based on support vector regression (SVR) for cost estimation for complex products in the early design phases. Tabu-SVR determines the parameters of SVR via a tabu search algorithm improved by the author. For verification and validation of performance on Tabu-SVR, the five common basic cost characteristics are summarized: accumulation, linear function, power function, step function, and exponential function. Based on these five characteristics and the Flight Optimization Systems (FLOPS) cost module (engine part), seven test data sets are generated to test Tabu-SVR and are used to compare it with other traditional methods (parametric modeling, neural networking and case-based reasoning). The results show Tabu-SVR significantly improves the performance compared to SVR based on empirical study. The radial basis function (RBF) kernel, which is much more robust, often has better performance over linear and polynomial kernel functions. Compared with other traditional cost estimating approaches, Tabu-SVR with RBF kernel function has strong predicable capability and is able to capture nonlinearities and discontinuities along with interactions among cost drivers. The third part of this dissertation focuses on semiparametric cost estimating approaches. Extensive studies are conducted on three semiparametric algorithms based on SVR. Three data sets are produced by combining the aforementioned five common basic cost characteristics. The experiments show Semiparametric Algorithm 1 is the best approach under most situations. It has better cost estimating accuracy over the pure nonparametric approach and the pure parametric approach. The model complexity influences the estimating accuracy for Semiparametric Algorithm 2 and Algorithm 3. If the inexact function forms are used as the parametric component of semiparametric algorithm, they often do not bring any improvement of cost estimating accuracy over the pure nonparametric approach and even worsen the performance. The last part of this dissertation introduces two existing methods for sensitivity analysis to improve the explanation capability of the cost estimating approach based on SVR. These methods are able to show the contribution of cost drivers, to determine the effect of cost drivers, to establish the profiles of cost drivers, and to conduct monotonic analysis. They finally can help designers make trade-off study and answer “what-i” questions. / Ph. D.