Quantile-Data Method For Value-at-Risk Based On Artificial Neural Network And Support Vector Regression

After the collapse of"Bretton Woods system", the price of stocks, foreign exchanges, interest rate and commodity fluctuated dramatically in a worldwide rage. The financial market appeared to be unprecedented frangible. Financial risk management became the most important point for financial institutes and business administrations, how to predict and control the market risks became the most urgent task faced by financiers. The financial risk means the uncertainty of the profit income or loss of the portfolios which financial institutes and non-financial corporations or individuals possessed. As common financial institutes, they keep bonds, stocks, investments and so on as a portfolio, the price of the portfolio always changes with the market factor. Especially, financial institutes nowadays, do not only deal with traditional financial products, but also keep liability and credits, and they use the complex derive instruments, such as futures and options to manage the risk of exchange and interest rate. Because the currents and the prices of all kinds of instruments often fluctuate with the foreign exchange, interest rates and market factors, it became an important problem that how market factors affect the price of the portfolios. The financial institutes take much care about the maximum possible loss of price of portfolios due to the market factor change.In this case, Value-at-Risk born, VaR is the maximum loss under certain confidence level during certain period. That's to say, VaR correspond to certain confidence level and certain period, it is the maximum profit loss of the portfolio with that probability. VaR is a new solution for financial risk, it can describe the potential loss of complex portfolio returns in the future market as just a float number. With VaR, financial institutes could recognize or even manage the possibility of the market risk which they expose to, survive from dropping into disadvantageous position or bankrupt. So far, there are many methods for VaR calculation, such as history simulation, Variance and Covariance method and Monte Carlo simulation and so on. Each method has some defects. History simulation is lack of agility, it can not show the loss which will be bigger than the biggest in the sample set; in addition, it's very sensitive to the capability of the sample set, the number of the samples will significantly affect the result, so users often need to collect many history datum for analysis and sometimes it's impossible. Variance and Covariance method always need to make a normal distribution hypothesis for returns, and what's more, an average assumption is often needed. But empirical data show that the distribution of compound return has several important characteristics such as kurtosis, fat-tailedness and skewness. So this method sometimes will underestimate VaR. Monte Carlo method do a very good job in precision, but it is too slow for some portfolio, and it often make a distribution assumption, this will lead to model risk.To solve the problems in VaR calculation, this paper proposed a new way for it, and developed two models. The second Chapter of this paper showed the history of Value at Risk, its conception and the significance in financial area, then this paper presented several popular methods for VaR: History simulation, Variance and Covariance method and Monte Carlo simulation etc. Monte Carlo simulation performs the best in precision. These methods can calculate VaR effectively in some way; however, they have their own defects. The third and the forth chapter of this paper introduce artificial neural network and support vector machine and their theory.The fifth chapter of this paper proposes two new methods for VaR calculation. The first is a quantile data mapping network based on artificial neural network, QDMN for short; and the second is a quantile data mapping network based on support vector regression, SVR-QD for short. QDMN and SVR-QD work with the principle that the artificial neural network and support vector regression perform well in nonlinear fitness. The two methods use the real market datum, attempt to fit the probability density distribution of the portfolio. The net structure and essential parameters are decided by theoretic proof and tests, and then VaR can be calculated. Both the two new methods use"Quantile-Return"(Qâ†'R) mode, whichs abandon the traditional"Distribution assumption - Parameter forecasting - Return calculation"mode."Qâ†'R"mode does not have any redundant process and speed up VaR calculation. In the last part of fifth chapter,"Qâ†'R"theory is described.In Chapter six, first of all, real market datum is analyzed. The conclusion of the analysis is that, in some case, the distribution assumption could not reflect the real world; sometimes they could mislead VaR calculation. These prove the necessary of our new methods. After this, the paper applies QDMN and SVR-QD to Shanghai Stock Exchange index for VaR calculation, and compares it to Monte Carlo simulation with four different distribution assumptions. The verification is done using Basle traffic lights, Kupiec's proportion of failure and VaR exceptions. In conclusion, QDMN and SVR-QD method based on"Qâ†'R"mode have better accurate than Monte Carlo simulation which has a distribution assumption and the underestimate rate is lower. QDMN and SVR-QD based on Qâ†'R method are two fast methods with high precision for value-at-risk calculation.The main contributions of this paper are:(1) Introduced several VaR methods, and analyze their advantages and disadvantages.(2) To overcome the defects in present methods, this paper propose a new model for VaR calculation: QDMN. QDMN works with the principle that the artificial neural network performs well in nonlinear fitness. The method uses the real market datum, attempts to fit the probability density distribution of the portfolio. The net structure and essential parameters are decided by theoretic proof (3) This paper proposed SVR-QD model for VaR calculation. SVR-QD also works with the principle that the artificial neural network performs well in nonlinear fitness. It is more exact than QDMN, but it converges more slowly. The simulation tests showed that QDMN and SVR-QD method based on"Qâ†'R"mode have better accurate than Monte Carlo simulation which has a distribution assumption and the underestimate rate is lower. They also perform better than history simulation and most analysis methods.