# cfai 2012 am exam q9B

Hi- the question asks whether the change in the price of the put option will be greater for an increase or decrease in price of the underlying and the answer was decrease.

So, for a call option, would this be the opposite?

Yes. Convexity at play. Long option holder benefits whether call or put

My brain is mush at this point, I’m struggling to think of the technical terms – just remember that an option has the highest gamma when it is at the money.

The option price/value will react more to a change in the underlying that brings the underlying’s price closer to the option’s exercise price . Whereas, the option price/value will react less to the underlying price moving away from the option’s exercise price.

Think about it this way – a call option is priced at \$1.00 with a strike price of \$100 for shares of XYZ and the shares of XYZ are trading at \$80. If the price were to change to \$90, the call option would change more in value than if the price of XYZ shares were to go to \$70.

in the example, the put option was out of the money. If the call option was out of the money, and the underlying asset changed in value, the call option would change more for an increase than a decrease in the underlying.

@theblackswan did my response make sense? Am i thinking about i the wrong way?

though your explanatio nis far easier

I actually answered the question not directly based on convexity but based on its closeness to strike price which will yield greater delta (moving closer to 1). Not sure how it will be graded on actual exam.

Yes u are right, same concept as in bonds.

also delta moves more than black scholes …for example if at 80 delta was 0.3, it my go to 0.4 at 90 but drop to only 0.22 at 70

do you mean towards -1 for puts?