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# Minyan Mailbag: Daily Volatility

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Hi John,

I remember a while back that you posted an article on volatility and how to calculate the daily, weekly or monthly, volatility from the yearly volatility (as part of an example of your trade). I was just wondering, was the calculation: the yearly volatility * sqrt(n/250) where n was the interval to calculate the new vol at?

Thanks,
Minyan Lloyd

Lloyd,

Yes. Just remember that you are dealing with linear math in a non-linear world. Linear math works on the average, so the real world looks and acts much different. In other words, just use this as a guide.

Regards,
Prof. Succo

Thank you for the reply John. I do understand that we're dealing with a non-linear world (thanks to your writings and Scott's).

I was wondering, is there a quick calculation that I can perform to determine (approximately) how much the price of an option will change with an x% change in volatility, with all things being equal (interest rate, time to expiry, stock price)? For example, if the volatility changes from say 45% to 30% but with no movement in the stock price (let's say after an earnings event that didn't do much). Or do I need to perform the whole black-scholes calc plugging in all the prices to solve for the missing theoretical option price?

Thanks. Keep it up with your great articles!

Minyan Lloyd

Lloyd,

It is not a straightforward calculation: you need the normal cumulative density function.

Vega is expressed as a price change in the option given a percent change in the volatility assumption. In this way we can compare how one option will change in price versus another option as the volatility changes.

It naturally follows that the larger the time premium of the option, the greater the vega so, longer term options have a higher vega than shorter term ones; expensive options have higher vega than cheap ones; at the money options have higher vega than in the money or out of the money.

Options, Futures, and Other Derivatives by John Hull can lead you through the derivation of BS and its components.

Regards,
Prof. Succo

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