# Derivatives question help

For three-month options on the FTSE 100 index, which of the following is likely to have the highest implied volatility? * A) A slightly out-of-the-money call B) A slightly out-of-the-money put C) A deep out-of-the-money call D) A deep out-of-the-money put

I am not sure, i think it is either A or B

D

^ For sure.

D for sure… Beyond the scope of the CFA exams though… At least from my experience…

why is the answer d?

Skew… Except for some commodities Put vol is higher than call vol…

Yeah. Why D? I thought it was between A or B. Correct me if I am wrong, I thought volatility is the rate of change of change===>Gamma. Isn’t gamma the highest when it is at-the-money?

Greeks are not necessary to answer the question. What you need to think is: which of this options is the most overpriced considering the probability of being in the money at expiration? A DotM option with a close expiry should be worth a very low value, close to 0, yet you see that sometimes it’s value is much higher. The higher deman for DotM put options comes from various factors including hedging, leverage and skewed returns…

ws Wrote: ------------------------------------------------------- > Yeah. Why D? I thought it was between A or B. > Correct me if I am wrong, I thought volatility is > the rate of change of change===>Gamma. Isn’t > gamma the highest when it is at-the-money? Nope - volatility is not a greek (though there is a greek which is about vol called vega which actually isn’t a greek at all but a cheesy 1970’s car or perhaps a fairly bright star but that’s a different story unless you insist on making it greek and then its kappa).

MrDonadei Wrote: ------------------------------------------------------- > Greeks are not necessary to answer the question. > What you need to think is: which of this options > is the most overpriced considering the probability > of being in the money at expiration? A DotM option > with a close expiry should be worth a very low > value, close to 0, yet you see that sometimes it’s > value is much higher. > > The higher deman for DotM put options comes from > various factors including hedging, leverage and > skewed returns… And prior to the 1987 crash, there wasn’t skew in equity index options? Amazing.

Joey or MrDonadei, thanks for the information. However, I am still not sure I know why D is the answer…would one of your explain to me? I read your post…however, I am still confused.

I’ve always assumed that OTM options had more volatility than ITM because of the lack of liquity in OTM. I’m told that this is not the case though…

I don’t think there is a mathematical explanation for it (but there might be). I think it’s more of a behavioral explanation that when you are talking about deep OTM options, there is probably more demand on the put side (for insurance) than on the call side. Skew may play into this by driving a higher need for puts than calls too because historically these have paid off better. Whatever the reason, there is typically more demand for deep OTM puts than equally deep OTM calls, driving up the premium over intrinsic value, and giving a higher implied volatility.

Or there are dozens of possible mathematical explanations.

^ yes, that’s a better way to put it.

TJR Wrote: ------------------------------------------------------- > I’ve always assumed that OTM options had more > volatility than ITM because of the lack of liquity > in OTM. I’m told that this is not the case > though… You’re confusing the volatility of the option price and the implied volatility of the option… Two completely different concepts…