Daily volatility forecasting methodologies: application and extensions

Abstract

Abstract Volatility plays a crucial role in portfolio management as well as derivatives pricing Reliable estimates of volatility are essential for trading strategies and Value at Risk calculations . Moreover even in derivative pricing models such as the Black-Scholes –Merton Model for option pricing the only parameter that cannot be directly observed is the volatility of the underlying asset (Hull, J. C.) Hence accurate estimates and good forecasts are necessary for implementation and evaluation of such models. Prices of assets such as stocks are known to exhibit a ‘behavior ’(Fama, E.F.) Models based on this random walk theory of stock prices imply that returns are normally distributed with a mean u and a constant variance . However it is observed that actual distribution of daily returns exhibits kurtosis with fatter tails than a normal distribution. The presence of thick tails can be explained by assuming conditional normality i. e. returns are normally distributed with the parameters changing everyday. Also the stock price returns show hetetoscedasticity i,e. variance changes with time and bursts of high volatility are seen intersperse with periods of low volatility . Also autocorrelation is observed in daily variance of stock prices(Engle, R. F.2001) The Generalized Autoregressive Conditional Heteroscedasticty (GARCH) genre of models is successful in capturing the effects of volatility clustering as well as conditional normality (Bollerslev, T.) GARCH with variations and for orders higher than(1,1) is used to model volatility of asset returns and give reliable estimates of daily volatility . This volatility estmate could be used to improve the performance of derivative pricing models as well as that of hedging and risk management. Moreover, Digital Signal Processing offers numerous signal prediction and estimation algorithms based on adaptive filter design. The project develops a technique to first de-noise or smoothen the volatility time series signal and then use a DSP-based technique to estimate the magnitude of the next sample of volatility brought about by daily news speculation ect. to derive an estimate of volatility of asset returns (in this case, volatility for the NIFTY from 1990 through 2006)