Three essays on modeling financial risk and pricing financial asset

This dissertation consists of three essays on evaluating and modeling market risk, prepayment risk, and interest rate risk, and pricing of financial assets.;Essay one: Using value-at-risk to control risk taking: How wrong can you be? This essay studies the biases in estimating Value-at-Risk when the sample errors in the estimation of variance-covariance matrices are systematically exploited. The essay studies the mechanism, distribution, and magnitude of these biases under three different assumptions about the motivations and behavior of the trader and find that value-at-risk estimates are systematically downward biased in all cases. In some circumstances the biases are large. The essay also proves that the distributions of the biases are independent of the underlining assets when no constraint is imposed. Imposing constraints on portfolio weight, such as no-short-sale constraint, can ameliorate the biases.;Essay two: A non-parametric prepayment model and valuation of mortgage backed securities. This essay estimates a mortgage prepayment model using a non-parametric technique called Generalized Additive Model. This approach is particularly useful in high dimension nonparametric estimations and in situations that involve mixed parametric and nonparametric specifications. The essay finds that the relation between prepayment rates and the main factors are highly non-linear and difficult to be captured with parametric functions. The decomposition of burnouts into expected and unexpected components improves the model fit and also has important pricing implications. The prepayment model estimated here fits the data significantly better than the extant models in the literature. The essay also prices mortgage-backed securities using the prepayment model and illustrates the pricing implications of the factors that affect prepayments.;Essay three: Nonparametric estimation of multifactor diffusion processes and its applications to Heath-Jarrow-Morton interest rate models . This essay develops a nonparametric estimation framework for multifactor diffusion processes with multivariate diffusion functions and applies it to multifactor Heath-Jarrow-Morton interest rate models. The nonparametrically estimated diffusion functions can help us to choose appropriate parametric functional forms of the diffusion functions and to determine the number of sufficient factors. It is found that a two-factor HJM model is in general sufficient and that the diffusion function for the first factor can not be reduced to a univariate function. The drift function under the risk neutral measure is estimated and compared with that estimated under the real measure, providing an estimate of the risk premium function based on historical data.