Modeling Returns and Unconditional Variance in Risk Neutral World for Liquid and Illiquid Market

Abstract

This article seeks to model daily asset returns using log-ARCH-Lévy type model which is expected to reproduce most of the stylized features of financial time series data (such as volatility clustering, leptokurtic nature of log returns, joint covariance structure and aggregational Gaussianity) that are empirically found in different types of market. In addition, unconditional variance of daily log returns in risk neutral world of different conditional heteroscedastic models is derived. A key observation is that liquid markets and illiquid market may not have the same underlying dynamics. For instance empirical analysis based on S&P500 index log returns as a liquid market do not have autoregressive part in their first moments while in Nairobi Securities Exchange NSE20 index there is strong presence of autoregressive dynamics of order three, i.e. AR(3). Higher moments of both markets are serially correlated.

Increments of Normal Inverse Gaussian Process as Logarithmic Returns of Stock Price

“…Probability density function of normal inverse Gaussian distribution is defined by the following equation: NIG distribution has higher kurtosis than normal distribution. It is very critical for many cases to accurately describe stock price dynamics [3], [4].…”

Option pricing using jump diffusion model: a case of stock markets of selected east African countries

“…These three markets are the largest stock markets in Africa. The study concentrated only on determining discrete jump dynamics but did not extend to options valuation and examine other stock features like leptokurtic Mwaniki (2015),. on the study using log-ARCH -Levy type model to study daily asset return, the empirical analyses of the Standard and Poor (S & P 500) index and NSE 20 index shows that in both markets features such as volatility and leptokurtic (features of financial time series data) were captured.…”