A Volatility Estimator of Stock Market Indices Based on the Intrinsic Entropy Model

Abstract

Grasping the historical volatility of stock market indices and accurately estimating are two of the major focuses of those involved in the financial securities industry and derivative instruments pricing. This paper presents the results of employing the intrinsic entropy model as a substitute for estimating the volatility of stock market indices. Diverging from the widely used volatility models that take into account only the elements related to the traded prices, namely the open, high, low, and close prices of a trading day (OHLC), the intrinsic entropy model takes into account the traded volumes during the considered time frame as well. We adjust the intraday intrinsic entropy model that we introduced earlier for exchange-traded securities in order to connect daily OHLC prices with the ratio of the corresponding daily volume to the overall volume traded in the considered period. The intrinsic entropy model conceptualizes this ratio as entropic probability or market credence assigned to the corresponding price level. The intrinsic entropy is computed using historical daily data for traded market indices (S&P 500, Dow 30, NYSE Composite, NASDAQ Composite, Nikkei 225, and Hang Seng Index). We compare the results produced by the intrinsic entropy model with the volatility estimates obtained for the same data sets using widely employed industry volatility estimators. The intrinsic entropy model proves to consistently deliver reliable estimates for various time frames while showing peculiarly high values for the coefficient of variation, with the estimates falling in a significantly lower interval range compared with those provided by the other advanced volatility estimators.

Does Volatility Cause Herding in Malaysian Stock Market? Evidence from Quantile Regression Analysis

“…Garman and Klass volatility is derived from the study of Garman and Klass (1980), which incorporates the maximum, minimum, (extreme volatility) and the opening and closing share prices. Vințe et al (2021) argue that Garman and Klass’s volatility is enhanced from Parkinson’s volatility because Parkinson’s volatility underestimates the opening jumps as it does not account for the opening stock prices. Hence, the Garman and Klass volatility is extended to include opening and closing stock prices as they argue that markets are more active during the opening and closing period.…”

The Cross-Sectional Intrinsic Entropy—A Comprehensive Stock Market Volatility Estimator

“…, for . We comment that Equation ( 4) contains in the right-hand-side term a linear combination between the CSIE component weighted with the variation between the close the open prices and the CSIE component weighted with OHLC variations , in the manner introduced for the intrinsic entropy (IE) volatility estimator [37].…”

“…Unlike volatility estimation using the IE model that we introduced in [37], the value was used for weighting the component , which quantifies the daily fine variations between the OHLC prices, while the difference was used for weighting , which accounts for the coarse variation between daily open and close prices.…”

Entropy Based Student’s t-Process Dynamical Model

“…With the use of finite samples from the background distribution , the posterior/filter distribution is inferred by the minimum principal for relative entropy, which is known as an entropy based particle filter [ 15 ]. The relative entropy (Kullback-Liebler divergence) between the filter distribution and the background distribution are defined as follows [ 23 , 24 , 25 ]: where is the domain of the dynamic latent variable . On the properties of the relative entropy as a quasi-distance for probability density functions, the filter distribution is obtained as the minimizer for the relative entropy in Equation ( 23 ).…”

“…With the use of finite samples from the background distribution Q(v, t), the posterior/filter distribution P(v, t) is inferred by the minimum principal for relative entropy, which is known as an entropy based particle filter [15]. The relative entropy (Kullback-Liebler divergence) between the filter distribution P(v, t) and the background distribution Q(v, t) are defined as follows [23][24][25]:…”