We propose a number of volatility measures that are based on ensemble averaging instead of time averaging. These measures allow fast measurement of current volatility without relying on series of past data (realized volatility) of future expectations (implied volatility). The introduced...

A Hidden Markov Model (HMM) is used to model the VIX (the Cboe Volatility Index). A 4- state Gaussian mixture is fitted to the VIX price history from 1990 to 2022. Using a growing window of training data, the price of the S&P500 is predicted and two trading algorithms are presented, based on the...

This paper will provide information on what happened in the financial crisis of 2008 and how to graph volatility outside of the option market. We will investigate the causes of the financial crisis, as well as some of the social inequalities that still exist today. We will explore household...

Topographic finance is the study of surfaces to describe financial systems in multiple dimensions. The problem with finance and economics is to describe accurately what is actually governing price dynamics. The price dynamics are behavioral and do not exhibit a rational maximization of a utility...

This paper is concerned with the problem of the estimation of the integrated volatility of log-prices based on high frequency data when both price jumps and market microstructure noise are present. We begin by providing a survey of the leading estimators introduced in the literature to tackle...

We propose a non-structural method to retrieve the risk-neutral density (RND) impliedby options on the CBOE Volatility Index (VIX). The methodology is based on orthogonalpolynomial expansions around a kernel density and yields the RND of the underlyingasset without the need for a parametric...

Financial markets face occasional shocks, which may come from geopolitical, economic, financial or other sources. In this paper, we consider the reaction of financial markets to the onset of severe conditions in the aftermath of Feb. 15, 2020. In particular, we analyze the primary and derivative...

Sudden and rapid changes in the economy leads to an increase in volatility. The fact that high volatility in financial markets brings along an increase in risk made it necessary to model it. Modeling volatility, which is accepted as a measure of risk, will benefit investors in their attitudes...

The study investigates the stock price movement of quoted Nigerian oil and gas firms using the Markovian model. Specifically, the study estimates the change in likelihoods and steady-state distribution of the share prices of the firms to determine the average time spent by the share price to...

This article provides the in-sample estimation and evaluates the out-of-sample conditional mean and volatility forecast performance of the conventional Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Asymmetric Power Autoregressive Conditional Heteroscedasticity (APARCH) and...