Calculating Stock Market Index Closing Value Using Risk Function Curve Equation, Logistic, B-Spline Curve and Polar Conversion Techniques

This paper discusses about the issues related to some strange behavior patterns in the financial markets that we term redundant sigmoid heterodoxy behavior of the financial markets. We test some basic empirical models employed to study these strange patterns emanating from fear of risk and panic that often belies as a true cause behind market crashes instigating dormant evolution before a full fledged recession and elucidate the interpretation as an outcome of such rigorous testing. In this otter, we developed a new model for measuring risk in order to identify true settings behind market risks by constructing a risk tolerance equation based on risk function curve and hence, to identify investor heterodoxy in the short run. Some novel statistical methods are employed in stock and equity market analysis for determination of Index Closing Values and volatility trends entailing the global markets. We use Risk Function Curves besides logistic functions and B-Spline curves to explain the events running down the line with a window toward Asia-Pacific and broad US markets. The functions deploy logical settings behind stock market trends and uncharacteristic movements correlated to the events having some major impact on the bourses. This paper applies new functions in understanding the mechanism of market failure and volatile behavior of stock markets as well as their movement trends both in the short and long run. The results stratify evidences that relate directly to the dynamics of stock/index movements thus giving an aid to investment managers a general view of the true nature behind volatility of these indices, as well as an aid in determining logical future index values