Comparing symmetric and asymmetric volatility estimates for S&P index prices

In every parametric formula of pricing a financial instrument, factors used in the calculation generally include the volatility estimate. Volatility measures the likely changes of the price for a specific period of time. The accuracy of estimated price strongly relies on the accuracy of provided expected changes in the market volatility for the period of interest. As opposed to other variables, which are assigned values to financial instrument, volatility is the only estimated one. For that reason, big focus of researchers was and still is on improving the volatility estimate. Initiated are different estimation approaches through last few decades. This paper explains few ARCH models, symmetric and asymmetric, and compares their estimates of daily volatility for the Standard and Poor’s Indexes.