🔎 Why does volatility increase the premium of an option?

Bruce argues that stock price volatility increases the premium of an option by providing two examples. The first example is for a call and the second is for a put.

When the stock is volatile/risky the Call option has a higher premium

Call with Low volatility: S varies between $360 and $480. (less volatile!) The maximum gain is $80. Premium comes out to only be $30

Call with High volatility: S varies between $320 and $520 (more volatile!) The maximum gain is $120. Premium comes out to be $40!

We see above that with a high volatility stock, the maximal gain is higher. Specifically, the maximal gain is $120 instead of $80. However, the worst gain is still only $0 because if the stock price goes down below $400, you won’t exercise the option. Therefore, the high volatility call is objectively worth more money.

When the stock is volatile/risky the Put option has a higher premium

Put with Low volatility: S varies between $360 and $480. (less volatile!) Premium comes out to only be $10

Put with High volatility: S varies between $320 and $520 (more volatile!) Premium comes out to be $20!

Once again, we see above that with a high volatility stock, the maximal gain is higher. Specifically, the maximal gain is $80 instead of $40. However, the worst gain is still only $0 because if the stock price goes above $400, you won’t exercise the option. Therefore, the high volatility put is objectively worth more money.