BSM - sensitivity factor

Vega: (Schweser, page.78)

…vega gets larger as the option gets closer to being at-the-money.

Why? Thanks.

Because at the money there is an abrupt shift between the intrinsic value of the option changing 1:1 (or -1:1) with a change in the price of the underlying, and changing 0:1 with a change in the price of the underlying. Far in the money it stays 1:1 (or -1:1), and far out of the money it stays 0:1.

Thanks, but Vega is discussing the volatility sensitivity. I understand Delta is most sensitive when the option price is at the money.

I was talking about vega: volatility sensitivity. Far out of the money or far in the money options won’t care much about volatility: the price change is 1:1 or -1:1 if the option is in the money, and 0:1 if it’s out of the money. But near-the-money options will care about volatility.

That is a very odd situation… So you mean to say options that are extremely out of the money have low vega? Makes sense as the volatility is not causing the stock price to reach the strike price. Who would you buy such a call with a situation like this.

Got it. Many thanks.

My pleasure.

It could be very cheap:)

And, with a low gamma, these options are useful for delta hedging.

Why useful?

I thought it’s only easier to hedge at low gamma.

I think that means the same thing…