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Explain the first method of calibration

Explain the first way of calibration if we can’t measure that parameter.

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Let’s see the first process in action. Examine, possibly, equity data to try to calculate what volatility is. The problem along with it is that this is necessarily backward looking, by using data from the past. It might not be relevant to the future. The other problem with it is that it might give prices which are inconsistent with the market. For illustration, you are interested in buying a certain option. But you think volatility is 27%, therefore you use that number to price the option and the price you determine is $15. Although, the market price of that option is $19. You can either choose that the option is incorrectly priced or which your volatility estimate is wrong.

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