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Volatility Smile

The Volatility Smile (VS) indicator is a chart that shows real-time price dynamics of options using the Black Scholes formula. Thus, we see in which direction market participants that use options in their strategies consider the movement the most likely.
The "Volatility Smile" indicator in the TVT platform is activated in the "Indicators" menu. VS takes as its basis the formula of Black Scholes, for the development of which the Nobel Prize in Economics was awarded. The calculation includes such parameters as futures price, market volatility, option premium, % funding rate, and time to option expiration. The main thing is that this tool shows the expectations of traders in the direction of growth or decline of the underlying asset. If the volatility smile is tilted to the right, it means that traders are expecting a rise more than a fall. If to the left, it means they are expecting a fall.
The X scale in the indicator window is the option strikes, the Y scale is the volatility percentage. Historical volatility is displayed as a % value under the curve. The more vertical the smile curve, the more expensive options are and the more investors fear or expect volatility.
If we take the S&P 500 futures, then puts will always cost more than calls on strikes equidistant from the current price, since the risks of a sharp fall for holders of large stock portfolios are always much greater than the risks of a sharp increase. But this is only valid for futures on the S&P 500 index.
As for the rest of the futures, the volatility smile will look different for different underlying assets. Since the time factor is taken into account in the calculation, the closer to expiration, the more vertical the curve, due to the fact that the cost of options in relation to the time of their remaining life is overestimated.
For example, if investors expect precious metals to rise, the volatility smile will be tilted up and look more vertical (right side of the indicator window).
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