Volatility (Finance) Explained - Derivatives

In finance, volatility (usually referred to as σ) is the historical volatility measured by a time series of past market prices. Implicit volatility looks to the future and is derived from trading in derivatives on the market. It is usually measured as a standard deviation of logarithmic returns and considers past and future. This is because over time, the probability increases that the price of the instrument will be further removed from the original price. Volatility increases linearly, and fluctuations are expected to equalize, so that the most likely deviation (twice as high this time) is not twice as large as the distance from zero. Gaussian random path (Vienna process), which follows the prices of financial instruments. This can lead to the price of the instrument rising or falling in the future. In today's markets, it is also possible to trade in volatility, but it does not measure the direction of price change. Volatility is measured only by the margin between price changes and is a parameter in the Black Scholes model. It influences the pricing of options because volatility is the difference between the market price and the actual price of an option on the stock market (e.g. a futures contract). The standard deviation (variance) is a variable that combines negative and positive differences, or the difference between market price and actual price. Two instruments with different volatility can achieve the same expected return, but the instrument with higher volatility will have greater fluctuations in value over a period of time. For example, a low-volatility stock has an expected average return of 7%, while a high-volatility stock with a standard deviation of 5% has an average return of 7.5%. The expected returns of high and low volatility stocks differ in the level of volatility. This would in most cases indicate the difference between the expected return of a stock with a standard deviation of 5% and high volatility of 7.5%. In most cases, this would indicate a difference of about 2.2% between a low volatility stock and a high volatility stock of 8.0% and 9.1%, respectively. This estimate assumes a normal distribution, but in reality shares are classified as leptokurtotic. It is common knowledge that all types of assets go through periods of high and low volatility, and that rapid price rises (a potential bubble) can often be followed by even higher (unusually high) prices. Phases of rapid price decline, such as the late 1990 "s and early 2000" s, are often followed by further declines known as "leptocorrelation," a period in which the price of a stock falls rapidly. Extreme movements usually do not come out of nowhere, but are indicated by larger movements than usual. Extreme movements are usually indicated not only by higher or lower prices, but also by a larger or smaller number of movements. This is called autoregressive conditional heteroscedasticity and corresponds to an increase in the rate of change in the price of a particular asset, such as a stock. Whether such large movements go in the same direction or in the opposite direction is hard to say, but the effect is observable, even if asymmetric. An increase in volatility does not always indicate a further rise; it may simply decrease. Not only the volatility depends on the measurement period, but also the time resolution and not only the size of the movement must be selected. By simplifying the above formula, it is possible to estimate annualized volatility based on approximate observations alone. The authors point out that realized volatility and implicit volatility are both backward and forward-looking - forward-looking measures, not reflecting current volatility. To address this problem, an alternative measure of volatility has been proposed, which appears to have bottomed out at 4%. It turns out that the risk-weighted volatility of a market portfolio that represents only a small fraction of a single investor's total market capitalization is much higher than the actual market value of that portfolio. Suppose you notice that the market price index, which is currently worth nearly $10,000, has been moving around 100 points per day on average for many days. This would be equivalent to an annual rate of 1.5% to 2.0% of the total market capitalization of the portfolio. This is because 16 is the square root of 256, which is about 1.5 times the total market capitalization of the portfolio. If you calculate this on an annual basis, multiply by 16 to get an annual volatility of 16%. The bottom line is that this crude approach underestimates true volatility by about 20%, and the VIX is left out. To measure volatility, we need to compare past volatility with the average size of the observations, which is about 1.5 times the total market capitalization of the portfolio. This is the average of all the variables of these observations and measures the difference between past and future volatility over a period of time. The blue line indicates the linear regression that leads to the displayed correlation coefficient (r). Note that the VIX has a very similar relationship to the average size of the portfolio, so the correlation coefficients are almost identical. Some critics claim that different data is used in this case to estimate and test the model, but others agree, claiming that they have not implemented the more complicated model correctly. I argue that when theory is about uncovering hidden principles that underlie the world, as Albert Einstein did with his theory of relativity, we must remember that models are metaphors and analogies that describe one thing relative to another. Practitioners and portfolio managers seem to completely ignore or reject volatility forecasting models.