Algorithmic Trading、RMBS Default Model And Their Applications

This thesis consists of two parts, algorithmic trading and residential mortgage default model. In the first chapter, we introduced the research background,research motivation and the structure and conclusion of the thesis. The first part contains chapter2 to chapter 5,discusses some hot issues in algorithmic trading,including the price-volume relationship,the forecast of the volume U shape curve,and the extensive study on the IS and VWAP strategy.The second part includes the six chapter, discusses the residential mortgage default model.Algorithmic Trading is placing orders through computer programs, that is to say, to determine the timing of placing the order, price, even the quan-tities of the order using the computer. Along with the development of the computer science and the investor’s demand for high return, together with the rich results in Theory of Stochastic Processes, in order to manage trans-action cost and risk better and hide the intension of investor, algorithmic trading research caused high attention from both the theory and practice field, and is growing fast.In this thesis, we report some recent results of our studies, discuss VWAP strategies and dynamic IS strategies separately and take rigorous empirical analysis on Chinese A share market data.We find the domestic market has a big impact cost, though utilizing the mathematic tools, we can make in-vestment strategies to replicate our investment goal using information till now.This part consists four chapters, whose main contents are described as follows:Chapter 2, in our thesis, the algorithmic trading strategy mentioned in this thesis refers the narrowly defined algorithmic trading. The estimation of the transaction cost become an important issue, in this chapter, we give some fundamentals theory, including the construction and estimation of the transection cost, the forge and the solution of the objective function.At last, we introduced the usual algorithmic trading strategy used internationally.Chapter 3, the volume-price relationship and the prediction of the price has always been one of criterions for stock selectivity and timing ability.There are rich results in this area.We consider both the two aspects.At first, we ex-amine the linear and non-linear relationship among the volume and price.Then we predicted the direction of the price change using the ordered-probit re-gression model. Also,the estimation for intra-daily volume profile is another important part for algorithmic trading, the most important reason is the intra-daily volume profile can help us split the order. We give some recent estimate methods.Finally, we give some result for comparison.Chapter 4, we do some extensive studies in two aspects.For one hand, we examined the forge and solution of the objective function for minimizing the static tracking error of VWAP strategy, we got the conclusion we should adopt the adjusted VWAP strategy because the positive relationship between the volatility and liquidity. For another hand, we studied the relationship of the mean-variance optimal VWAP strategy and minimum variance VWAP hedging strategy under the stochastic process theory and find the the mean-variance optimal VWAP strategy can be thought an sum of minimum vari-ance VWAP hedging strategy and a directional adjustment related to the price process.Chapter 5, we discuss IS strategy which is most discussed. As traditional IS strategy does not consider the impact of U shape intra-daily volume profile curve, we analysis the adjustment according the U shape curve.Then we consider the dynamic two stage model in which the trading strategy is not determined before, but is adjusted based on the information of the first half trading interval.At last, the chapter consider the IS strategy under another risk criterion-aggressive VaR criterion.In the second part, we examined the RMBS (residential mortgage backed security) default model. U.S. Subprime Crisis triggered the global financial crisis. It made banks have to strengthen their risk control. The main risk of banks is credit risk, and mortgages are the major part of bank lending. In this paper, we gave two quantitative models-Logistic regression model and Cox proportional hazard model. Finally, we used both of them to model mortgage data in one state in the United States. We compared the results, and we can see that the Cox proportional hazard model can not only give borrower’s default risk measure for each time point (or loan age), but also has high accuracy and robustness relative to Logistic regression model.