# Volatility modelling

### Volatility modelling.

Before anyone begins trading in assets, there is one fact that you are always warned about-assets are volatile. This  is the sheer truth behind  all assets that you would want to trade. People have lost money because of this volatility  in the market. It is related to the fact that  one cannot get to know what will happen in the market. However, with a deep analysis, one can make money from asset trading. Modelling the assets can be one way in which we mitigate these risks. Volatility modelling is, therefore, the development of mathematical models, which can be used to predict the market movements.

Types of volatility models

In general, volatility models can be divided into two. That is conditional variance volatility models and stochastic volatility models.

Conditional variance volatility models make use of variance in their functions while stochastic volatility models  are functions, which are not purely  observable. Stochastic models can be referred to as latent models. The term stochastic is a statistical term that implies  randomness in the distribution. From the definition, it is easy to infer that the variance in the distribution of these models is random.  Stochastic volatility models are used to correct the deficiency of the black-Scholes model, which assumes that the variance of the underlying stock is constant. The various types of stochastic volatility models are the GARCH models, SABR models, Heston models, and CEV models. Examples of conditional variance models are ARMA models.

ARMA MODELS.

ARMA model is an abbreviation for the autoregressive moving average. As you might recall from your time series analysis, it is formed when the two models autoregressive and moving average, are combined.

They model stationary time series data of stock. Stationarity must be satisfied before using the data. If it is not satisfied, differencing could be applied to make it stationary if differencing is applied the name of the model shifts to ARIMA models. The inclusion of the letter I is for the differencing applied to the data.

A crucial disadvantage of this model is that it assumes a constant variance, whereas, in real life, it is not.

GARCH models.

This econometric volatility model was coined in the early 1980s by Robert F Engle and provided a way to estimate the volatility of most financial assets. Most financiers prefer it as it provides a more accurate results compared to  any other volatility model.  The process of fitting a model can be accomplished in three steps, which are fitting an autoregressive model, computing the autocorrelations in the error terms and finally testing for significance.

Heston models.

This is a statistical model named after Steve Heston, who first proposed this model. Under this model, the volatility of the assets is assumed to be arbitrary.  The model is used for pricing of the European options.  What differentiates these models from the other stochastic volatility models isthe features that  it does not require a log-normally distributed data; it factors in the possibility of a correlation between the volatility and the stock’s price.

SABR models

This volatility model is an abbreviation of the words stochastic, alpha, and rho, which are the parameters used in this equation.  It models the volatility of financial derivatives.

CEV models

Constant elasticity of variance or CEV models are stochastic models, which provide an alternative to the black-Scholes option pricing models.  It was developed in 1975 by John cox and is widely used by financial practitioners.

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