We introduce extensions of the Realized Exponential GARCH model (REGARCH) that capture the evident high persistence typically observed in measures of financial market volatility in a tractable fashion. The extensions decompose conditional variance into a short-term and a long-term component. The...

This paper investigates the forecasting performance of three popular variants of the non-linear GARCH models, namely VS-GARCH, GJR-GARCH and Q-GARCH, with the symmetric GARCH(1,1) model as a benchmark. The application involves ten European stock price indexes. Forecasts produced by each...

The first ever explicit formulation of the concept of the option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True...

Volatility is widely considered to be a category of technical indicators with a simple interpretation - no matter how it is measured volatility is widely believed to rise in a market downturn. This approach is applied to indicators such as the Average True Range (ATR), Bollinger Bands®...

The first ever explicit formulation of the concept of an option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True Value-at-Risk...

• It is not widely emphasized in the literature that derivatives are complex random quantities which should, by custom, be characterized by their probability density functions. • It is understood that Black-Scholes style of derivatives pricing represents an expected value, i.e. the...

ARFIMA models, as advocated by Jiang and Tian for use in long-term volatility forecasting, are found in a follow-up empirical study to be dominated by a certain simple historical predictor of stock price volatility at a five-year horizon. (This particular historical predictor is not recommended...

In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Itô semimartingale. We adapt the principle idea of regularization from linear regression to covariance estimation in a continuous-time high-frequency setting....

The article presents a quantitative strategy in which comparison of short-term asset price movement with corresponding middle-term asset volatility is used for determination of the size of opening position when buy signal is obtained from trend following model. The strategy is named as...