Study on Fuzzy Factor GARCH Model

Abstract

As known to all, securities market is easy to be affected by subjective consciousness and its largest characteristic is uncertainty. Similar to financial market, securities market can be influenced by politics, economy and society, causing return on assets and investment risk to change constantly and to be difficult to describe. As a result, it forms strong fuzziness. Based on the hypothesis of fuzzy rationality, fuzzy rule if-then is applied in the paper to improve traditional factor GARCH model through the thought of fuzzy mathematics.
Firstly, Gaussian membership function is constructed for stock return to calculate the covariance matrix of multiple fuzzy number of return on assets and principal component analysis (PCA) and statistics means are utilized to model revenue volatility. Finally, applying fuzzy factor GARCH model to revenue volatility of stock and to estimate various parameters.
It mainly conducted research on volatility of revenue of financial data by means of factor GARCH model in previous studies but neglected the fuzziness of financial market. In this paper, perspective of fuzziness takes place of randomness and relevant techniques including fuzzy mathematics, analysis of time series and PCA are used to transform factor GARCH model.
In the Markowitz model for portfolio investment, it implicitly assumes that investors perform one-period investment: there are only a certain number of capital funds before making decision and not any securities, but it is not consistent with the real situation. The logical hypothesis is that the process when investors make decision on portfolio investment is their readjusting volume of holdings of different securities and meanwhile remaining capital funds unchanged.
For securities that generate relatively steady revenue and have low risk exist in the financial market, portfolio needs to meet the requirement of securities market and investors. In this paper, former mean of return is taken as the expected return of assets and evaluation of risk matrix and upper and lower probability of quadratic programming model of portfolio is created to help investors to use investment strategy in a better way.