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Write this down: Changes in volatility means changes in option price. It doesn’t matter if it’s a put or a call, front month or back; in the money or out -of- the-money, it doesn’t matter. If volatility goes up, the prices of options go up. Likewise, if volatility goes down, option prices go down.
 
Volatility not only prices but also affects all the Greeks. Out-of-the-money Delta increases but in-the-money Delta decreases. When volatility decreases, the opposite happens: in-the-money options gain Delta and get more in-the-money while out-of-the-money options lose Delta and value. (Academics call this Trumpification.)
 
As volatility increases, it increases the amount of extrinsic value (time value). When the amount of extrinsic value increases the amount of decay increases; the bigger the extrinsic, the bigger the decay; it’s as simple as that. The opposite also is. When volatility decreases, extrinsic value of the option also decreases. If there is less extrinsic value, then there is less time decay required to reach zero at expiration.
 

Volatility can have a profound effect on the shape of the normal distribution curve.

 
 insert fig6-1
 
The more range of variance from the mean ($ 60) the more volatility. More volatility normally means higher option prices. Moreover, as Ron Ianieri of Options University points out, without volatility there can be no option. When an option is out-of-the money, it has extrinsic value and this changes as a function of the pricing model. But when the OTM option expires, there is no extrinsic value because time to expiration is zero; no extrinsic in an OTM means their is no option. On the other hand, when an option is deep in-the-money it acts just like the stock and has no extrinsic value. The option now is just like holding the stock. For options deeply out-of-the money, they have no real extrinsic value. So, without extrinsic value and its corresponding volatility, there is-in effect-no option. When deep ITM the option is the same as the stock; way OTM has little to no extrinsic value so that also is not an option.
 

In summary, wider price movements means more volatility. More volatility means higher option price because big moves have a supposed higher capability to move into-the-money. By the same token, high volatility can mean more probability of moving out-of-the-money.

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