As a trader, I want to make money through day trading which is possible only if there’s a huge fluctuation (Volatility) in the market. Because when prices keep moving up and down you will be able to long or short frequently mapping the vicissitudes in the market. In FRM-I we will cover volatility in topic – VaR.

Volatility in brief:-
Estimating Volatilities and Correlations
In the field of finance, volatility measures variation in prices of a financial instrument over time or a measure of dispersion of returns for a given security or market index. If the stock price moves up and down rapidly in short intervals of time, it implies high volatility. If, however the price remains constant, it has low volatility.

In this session, you will learn how to produce estimates of current and future level of volatilities and correlations.
  • What is the current volatility?
  • What is it likely to be in future?
  • How do we forecast something we never observe?

To find out answer to first question about current volatility, there could be two possible choices:
  • Find out the standard deviation over the last ten years. This could be used as a proxy for current volatility. However, it will include lots of old information that may not be relevant for short term forecasting.
  • Other option could be to find out the standard deviation over the last ten days unlike ten years above. But, this value will be highly variable because there is too little information.

ARCH Model (Auto Regressive Conditional Heteroskedasticity)
  • This model predicts the variance of returns on the next day and relies on two features of returns i.e. volatility clustering and mean reversion of volatility.
  • In this model, we use a weighted average of the volatility over a long period, placing higher weights on the recent past and small but non zero weights on the distant past.
  • Similar to ARCH is EWMA model except that the weighting parameters used in EWMA follow a particular pattern as discussed below.
EWMA (Exponentially weighted moving average model)
  • In EWMA, the weights thus assigned decline exponentially as we move back through time.
  • EWMA is relatively attractive as:
    • Comparatively little data needs to be stored.
    • We only need to remember the current estimate of the variance rate and the most recent observation on the market variable.
    • It also tracks volatility changes with a parameter called lambda as the sensitivity to current changes in market variable.
From simple ARCH to GARCH
  • GARCH or Generalized ARCH is an obvious extension of ARCH.
  • In GARCH, tomorrow’s variance is predicted to be a weighted average of the
    • Long run average variance
    • Today’s variance forecast
    • Today’s squared return
  • It allows us to predict volatility term structure changes.


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