In the early stage, the fixed exchange rate policy was established in Taiwan, with focus on the exchange of NT Dollar to US dollar. After undergoing the changes of flexible exchange rate system, the regulation of exchange rate gradually renovates. On January 30, 1991, the exchange rate system changed to a managed floating system that allows the exchange rate to be more liberal. The spot USD trading price is no longer restricted by the upper or lower limit among banks, and the negotiation of trading price is completely free. As the exchange for NTD to USD becomes more liberal, the issue of the factors behind the price fluctuation on NTD to USD has become an interesting subject to study. This paper investigates Taiwan¡¦s foreign exchange market in order to discover the factors that cause the price volatility, whether it is private information or macroeconomic news announcement of public information. This study examines the exchange rate occurred every 15 minutes during January 5, 1992 to November 27, 2001. Given the result that the increase of macroeconomic news announcement does not increase the volatility, the volatility in Taiwan¡¦s foreign exchange market is mainly caused by private information, not public information. Although the return variance is comparatively higher than the return variance in other normal time period during the macroeconomic news announcement, the highest return variance before the trade close does not occur at the time of public news announcement. It represents that the occurrence of volatility is not affected by the macroeconomic news announcement. If foreign exchange volatility is not affected by macroeconomic news announcement of public information, then private information might be the major factor affecting the price volatility. The findings are as follows: 1. The volatility in trading period is much higher than the volatility in non-trading period, demonstrating the existence of ¡§exchange message effectiveness¡¨. Meanwhile, it also states that public information is not the only information existing in the market. Even at the most efficient market, the informative pricing has reflected all the public information. The macroeconomic news announcement of public information would not affect the price volatility, the asset pricing volatility is affected by the private information. 2. Trading time become longer which makes the informed trader not necessary to trade in a hurry, diverging the volatility of transaction. 3. The volatility at closing period increases because of the occurrence of private information. It may downgrade to public information during non-trading period. People holding valuable private information would trade before the market is close. Concluded from above, it can be discovered that the private information has played an important role incurring the large volatility in Taiwan¡¦s foreign exchange market.

The aim of this thesis is to improve risk measurement estimation by incorporating extra information in the form of constraint into completely non-parametric smoothing techniques. A similar approach has been applied in empirical likelihood analysis. The method of constraints incorporates bootstrap resampling techniques, in particular, biased bootstrap. This thesis brings together formal estimation methods, empirical information use, and computationally intensive methods. In this thesis, the constraint approach is applied to non-parametric smoothing estimators to improve the estimation or modelling of risk measures. We consider estimation of Value-at-Risk, of intraday volatility for market risk, and of recovery rate densities for credit risk management. Firstly, we study Value-at-Risk (VaR) and Expected Shortfall (ES) estimation. VaR and ES estimation are strongly related to quantile estimation. Hence, tail estimation is of interest in its own right. We employ constrained and unconstrained kernel density estimators to estimate tail distributions, and we estimate quantiles from the fitted tail distribution. The constrained kernel density estimator is an application of the biased bootstrap technique proposed by Hall & Presnell (1998). The estimator that we use for the constrained kernel estimator is the Harrell-Davis (H-D) quantile estimator. We calibrate the performance of the constrained and unconstrained kernel density estimators by estimating tail densities based on samples from Normal and Student-t distributions. We find a significant improvement in fitting heavy tail distributions using the constrained kernel estimator, when used in conjunction with the H-D quantile estimator. We also present an empirical study demonstrating VaR and ES calculation. A credit event in financial markets is defined as the event that a party fails to pay an obligation to another, and credit risk is defined as the measure of uncertainty of such events. Recovery rate, in the credit risk context, is the rate of recuperation when a credit event occurs. It is defined as Recovery rate = 1 - LGD, where LGD is the rate of loss given default. From this point of view, the recovery rate is a key element both for credit risk management and for pricing credit derivatives. Only the credit risk management is considered in this thesis. To avoid strong assumptions about the form of the recovery rate density in current approaches, we propose a non-parametric technique incorporating a mode constraint, with the adjusted Beta kernel employed to estimate the recovery density function. An encouraging result for the constrained Beta kernel estimator is illustrated by a large number of simulations, as genuine data are very confidential and difficult to obtain. Modelling high frequency data is a popular topic in contemporary finance. The intraday volatility patterns of standard indices and market-traded assets have been well documented in the literature. They show that the volatility patterns reflect the different characteristics of different stock markets, such as double U-shaped volatility pattern reported in the Hang Seng Index (HSI). We aim to capture this intraday volatility pattern using a non-parametric regression model. In particular, we propose a constrained function approximation technique to formally test the structure of the pattern and to approximate the location of the anti-mode of the U-shape. We illustrate this methodology on the HSI as an empirical example.