A New Measure of Volatility Using Induced Heavy Moving Averages

Abstract

The volatility is a dispersion technique widely used in statistics and economics. This paper presents a new way to calculate volatility by using different extensions of the ordered weighted average (OWA) operator. This approach is called the induced heavy ordered weighted moving average (IHOWMA) volatility. The main advantage of this operator is that the classical volatility formula only takes into account the standard deviation and the average, while with this formulation it is possible to aggregate information according to the decision maker knowledge, expectations and attitude about the future. Some particular cases are also presented when the aggregation information process is applied only on the standard deviation or on the average. An example in three different exchange rates for 2016 are presented, these are for: USD/MXN, EUR/MXN and EUR/USD

Analysis on the Possibility of Investment in the Mexican Emerging Market

“…Also, some macroeconomics variables like GDP, interest rate, foreign reserves can affect volatility as well [8]. In addition to standard deviation, volatility has other variations, like using induced heavy moving averages [9], implied volatility, and using non-overlapping monthly volatility [12]. In this paper, the USD/MXN volatility in 2019 is calculated by using a standard formula of daily changes.…”

“…In this paper, the USD/MXN volatility in 2019 is calculated by using a standard formula of daily changes. This information may be useful to forecast volatility in 2020 and can be used to compare with weighted volatility, which uses different extensions of the ordered weighted average (OWA) operator [9]. The exchange rate peso per US dollar has a slight fluctuation during the past year.…”

“…Volatility is an important factor when forecasting the future foreign exchange market. Risks bought by new strategies when exchange rates change can be predicted to some degree [9]. Forecast of volatility is important to market participants when they make decisions and many kinds of model use forecasts of volatility as a vital factor, like the option pricing model introduced by Black and Scholes [5].…”