When the option is at the money slight changes in the volatility of the underlying asset will have greatest affect on the probability of the option being in the money at expiration. Can anyone explain? thanks
If you have an option to buy a stock at $10 and the current stock price is $20, then the value of the option will not be very sensitive to changes in the underlying (and hence the volatility of the underlying) - the option is deeply in the money, so if the stock price moves from $20 to $21 or $22 has little impact on the option value. The same is true when the option is deeply out-of-the-money - at a strike of $10 and a stock value of $2, the option is worth nothing and that won’t change if the price of the stock moves to $3 or $4. If, however, the stock price is $10, so at strike, a move in the underlying to $9 means that the option value is zero while a move to $11 means that it’s in the money. So “at the money” the option is most sensitive to changes in the underlying.
Think in terms of positive negative payoffs. As the guy before me has explained, you swing back and forth when the option is at-the-money. When you are deep-in or deep-out, a little volatility wouldnt change the payoff between positive and negative payoff.
Because gamma is highest at the money. The option is very sensitive to its inputs at this point.