How to grasp uncertain events

Commercial bonds development and asset management came to must manage uncertainty in financial market, that introduced stochastic model to deal with the problems how to grasp future uncertain events of economic changes and corporate activities.

The important point is a basis of component of the stochastic distribution reflects effectiveness, reliability of modeling, how to grasp the events, in response to real society.

An applied model under uncertainty is only an approximation of real events. The prediction presumes future data by use of past data. In case of using a model for prediction, the choice of a model decides precision of prediction.

Stochastic modeling and evaluation standard of prediction apply for the stochastic model in financial market. The choice of a model decides precision of the prediction which model using to approximate real market behaviors. The model is always approximation of real world with exceptional events contained uncertainty.

Effectiveness of the model and modeling rely on a design of stochastic distribution dealt with uncertainty.

Described as risk management in another pages, the price change distribution of various underlying assets that are components of portfolio can approximate same historical volatility by same historic data. But different underlying asset price changes are not same. So that a precision of approximation and reliability are not in complete, there is always a premise of an assumption. The assumption is price changes depend on the normal distribution( Gaussian distribution). Real world price distribution, for example historical changes of foreign exchange rate, shows a fat tail distribution that is well-known. As far as the VaR is based on the normal distribution, there is a method to mix each asset historical distributions in order to approximate real events. The GARCH method assumes that each asset price changes or the expected return of investment depend on the conditional multi-various normal distribution at each time.

The GARCH model assumes a variance depends on the square of epsilon of historical data or historical variance. It shows experiences data as mixing stochastic variables with different means and variances.

European application mathematicians proceed to positive study by such an approach in the area.

Even if general normal distribution is used for VaR model, in case of leveraged derivatives embedded in the component of the portfolio, the derivative for the purpose of risk hedging might become a fluctuation factor of the portfolio. For example, if all investors in the market have same portfolio, market risk extends to all investors then extreme fluctuation damages the portfolio.

The sub-prime problem is a similar example.

There is a similar structural market for investor’s portfolio to such an example in a specific category.

The market holds structural uncertainty that could not show the only percentage of VaR by historical volatility. Once market changes in one direction, the investor’s portfolio accepts extreme change due to the market structure. However the market structure does not reflect historical volatility until it happens.

Introducing VaR as a stochastic model for risk management, it is necessary to recognize the feature and the premises of VaR that principal stochastic model approximates by the normal distribution. The reliability of risk management is up investigating the precision of VaR approximation from different point of view for the portfolio behavior.