Scenario Generation In Dynamic Investment Portfolio Based On Stochastic Programming

Stochastic Programming Model (SPM), as a powerful tool, has been widely used to such financial fields as asset allocation, Asset and liability management (ALM), and securities' portfolio management and so on. SPM need generate many scenarios simulating future uncertainty of which scenario tree acted as input to stochastic optimization is constructed on basis. The global optimal solution of model is the basis of decision-making advices for financial programming. So, the description of uncertain economic scenario plays a great role in the success of the decision-making in multistage investment portfolio. This paper focuses on study of several models for scenario generation. The main research work and conclusions is as following:1,building the scenario generation model based on GARCH model.GARCH family models can depicts the following phenomena of asset return in financial market: volatility clustering, non-asymmetric, leptokurtic features. The paper utilizes these advantages to build the corresponding AR and GARCH models according to the respective asset kinds' features. The main work done here includes four aspects: scenario generation model based on univariate GARCH model. Scenario generation model based on multivariate GARCH model. Comparison of the two kinds of models in statistics. Construction of two-period scenario tree.The numerical result shows that the two kinds of GARCH models can produce scenarios with similar statistical attributes to historical data which tells us that the GARCH family model is sufficient to scenario generation. Secondly, the multivariate GARCH model has a better performance than the univariate one maybe for the reason that it can take the correlation among the assets into consideration. However, multivariate GARCH model also has a disadvantage, much too complex model structure and difficult parameter estimation. Univariate GARCH model can replace multivariate one when the correlation among assets are small.2. Single variable moment-matching scenario generation model.Hoyland and Wallace firstly give a common framework to generate scenario based on moment-matching which builds a scenario tree by solving a non-linear optimization model and getting the value and probability of scenario. It has some pitfalls such as local optimal solution and arbitrage opportunity existence and so on. The work here improves the above model which includes three aspects: study of Single variable moment-matching scenario generation model; how to avoid the arbitrage opportunity; how to depict the descriptive features and another idea of scenario generation based on moment-matching.Single variable moment-matching scenario generation model takes the probability of the scenario's value as the variable decided and construct the single-period scenario tree by approaching the four center moment of historical return data and then generate multistage tree with the help of VAR model. The article adds a constraint to solve the problem of 'descriptive feature' ignored in scenario generation in the long term. Besides the above, the idea of 'partition of return interzone' assures that it can avoid arbitrage opportunity.The second way is to produce one random variable's discrete marginal distribution once and then produce a joint distribution on the basis of all the produced discrete marginal distribution, finally, approaches the aimed moment and correlation matrix by all kinds of transforms. Empirical study shows that this way avoid vast numerical computation and can get the scenario with much similar statistical feature of the historical return.3. Research on generating scenario by clustering and application.K-means clustering can partition large set of data and build a single-level class, dividing the sample data into K independent clusters as the asset return scenario. The research work here tries this way to generate scenarios and compare it with the way of moment-matching statistically. The result here shows that this method tries not to rely on model to produce scenario but to find the correlation between asset returns from historical data. At the same time, the article gives a linear programming method that adding a scenario in order to avoid arbitrage. The empirical study shows that the way not only has the advantage of moment-matching way, but also has improved in depicting statistical features, which can much more accurately depict statistical features through much less scenarios. The methods lay the foundation for decreasing the size of problems by much less scenario, especially introduces a new idea for multistage scenario generation.4,Research on scenario generation based on VAR and its applicationVAR model is a usual way for financial data analyzing and often used to forecast connected time serials system and analyzes dynamic impulsion to variable system by random disturbance. The research work here includes construction of proper VAR model of four indexes' return; Production a lot of scenarios by Monte Carlo simulation, Comparison of the effect between VAR and multivariate GARCH model; Constructing a 2-period scenario tree.The research result shows that VAR models performs better than multivariate GARCH model for its CDF is nearer to historical data than the multivariate GARCH model. Besides that, VAR models are simpler. It not only demonstrates the correlation among variables and periods. So it is a excellent way for scenario generation.5. Scenario generation based on Copula function.Copula function mainly has three advantages as follows: it can flexibly construct multi-dimension random variable joint distribution; it can accurately depict nonlinear correlation; It can can overcome the limitation of the normal distribution hypothesis of assets return. Here this article does the following research work: Bring forward a comprehensive way to generate scenarios based on Copula function, GARCH model and extreme value theory; Compare its scenario effect with VAR and clustering. The numerical test shows that the way proposal by us is a more reliable method than the other two ones.