Out of Money Option to hedge

CFA Level II Derivatives
#1

Hi all,

Can anyone explain what is going on in question 48 CFAI Mock PM? I can’t understand what’s the question and answer talking about.

For simplicity:-

http://imgur.com/a/dTZuZ

#2

Lets assume the current price is 750. Therefore if strike is >750 it is an out of the money call (and an in the money put) and strike<750 is an out of the money put (and an in the money call).

Since options with strike <750 have higher vol, and higher vol = higher option value, out of the money puts are more expensive than out of the money calls (i.e. establishing a long position with options)

Is the answer A?

#3

yes the answer is A.

I don’t understand the hedging and establishing long position part.

Is this means:-

buying put=using option to hedge? if yes, can you explain why please?

Establishing a long position = buy call? if yes, can you explain why please?

#4

I’ll start by saying that I’m an options trader and most of the CFAI questions on options are an abomination. That said…

Yes, all they’re asking in this question is for a relative comparison of “cheapness” by looking at the implied volatilites. In this instance, it wasn’t exactly clear if the stock was trading at 750(given in the vignette there was a scenario where the index dropped by 10%, but this was assumed to be the base case of a 750 price). So, if the index is at 750, you would take a long position via out-of-the money options by buying calls, and hedge a long via out-of-the money puts. Given that the implied volatilites at each strike above 750 are lower than those below it, in theory it would be “cheaper” to take a long position via calls than hedge a long via puts. In the real world, implied volatility structures look nothing like this, but I digress.

#5

Why would options with a strike price less than 750 have higher volatility than those with a strike greater than or equal to 750?

The volatility in, for example, the B-S-M option pricing model is the standard deviation of the (continuously compounded) returns on the underlying; that number is the same irrespective of the strike price on any option you might buy or sell.

#6

Please read the question