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 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...

The rough path-dependent volatility (RPDV) model (Parent 2022) effectively captures key empirical features that are characteristic of volatility dynamics, making it a suitable choice for volatility forecasting. However, its complex structure presents challenges when it comes to estimating the...

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 focuses on modeling the evolution of volatility deterministically through (G)ARCH models and compares the performance of the different models, using the daily bilateral prices of one USD to 1 Euro from January 04, 1999 until June 23, 2017. It also compares the performance of these...

This paper tests whether volatility for equity returns for emerging markets possesses long-range dependence. Furthermore, the assertion of whether long-range dependence is time-varying is checked through a rolling sample approach. The empirical results suggest that there exists long-range...

This paper extends research by Batten and Ellis [Econ. Lett. 72 (2001) 291] to propose a simple model of scale-adjusted volatility which measures the extent to which the Gaussian scaling law mis-estimates long-horizon volatility. Applied to the Dow Jones industrial average, the results of our...

Short time series are fundamental in the foreign exchange market due to their ability to provide real-time information, allowing traders to react quickly to market movements, thus optimizing profits and mitigating risks. Economic transactions show a strong connection to foreign currencies,...