The Study Of The Non-linear VaR For Options Portfolio Based On Numerical Dimensional Reduction

In the last 20 years financial derivatives and financial derivatives market have been developed rapidly. Futures and options are now traded actively on many exchanges throughout the world. Derivatives are generally used as an instrument to hedge risk, but can also be used for arbitrage purposes. Their features, such as leverage, low cost and high liquidity, result in new risk for investors. Meanwhile, warrant which is similar to options have been issued and traded again at home in July 2005. After four years of rapid development, the warrant market in China has taken shape. In 2008 the trading volume of Shanghai and Shenzhen exchange market has excess 6.97 trillion. Correspondingly, how to measure and manage market risk become a realistic problem.Value-at-Risk has become widely used by corporate and fund managers as well as by financial institutions. It is an attempt to provide a simple number summarizing the total risk in a portfolio of financial assets. However, the traditional non-linear VaR models, which measure market risk for portfolio of options, are generally based on the assumption that distribution of risk factors is normal. It is difficult for a portfolio of various options to estimate VaR using these models. Therefore, the dissertation presents a improved non-linear VaR models in the perspective of dimension reduction. The detailed research contents of this dissertation are as follow:First, the dissertation introduces the definition of options and difference between options and warrants. Then the development of warrants market in China mainland, Hong Kong and some foreign countries is reviewed.Second, the dissertation builds O-GARCH model with the assumption of student's t distribution for risk factors aims to avoid problems caused by historical volatility models. Meanwhile, the model avoids over-abundant parameters which are difficult for traditional multi-GARCH model to estimate. The underlying shares of Shanghai and Shenzhen warrants are examined by the model. Then comparing with EWMA, CCC and O-GARCH model, we follow two criteria to judge the quality of the volatility forecast.Third, in according to Black-Scholes model based on student's t distribution and O-GARCH model, the Greek letter is calculated in this dissertation. We derive non-linear VaR model based on the basis of fast Fourier transform and convolution formula. In empirical analysis, we make a comparison between this model and local Monte Carlo method. The result shows that the model is as accurate as local Monte carol and is more efficient than the one.Finally, we derive two dimension reduction methods to improve efficiency of convolution VaR model. The asymmetric Laplace distribution is fitted for risk factors in the model. Next we analyze empirically portfolio of China mainland warrants and Hong Kong warrants. The result shows that low rank method based on student's t distribution costs less time and smaller error. According to Kupiec test and MRSB, we test the VaR evaluated by dimension reduction method and conclude mean square error method based asymmetric Laplace distribution is more efficient.