## FRM II-MR

anbu.edu
Finance Junkie
Posts: 205
Joined: Mon Feb 04, 2013 3:35 pm

### FRM II-MR

With all other things being equal, a risk monitoring system that assumes constant volatility for
equity returns will understate the implied volatility for which of the following positions by the largest
amount:
Select one:
a. Short position in an at-the-money call
b. Long position in an at-the-money call
c. Short position in a deep in-the-money call
d. Long position in a deep in-the-money call

Why cant the answer be C

edupristine
Finance Junkie
Posts: 704
Joined: Wed Apr 09, 2014 6:28 am

### FRM II-MR

Hi,
The answer to this question would be (d) as explained below:

We already know that Strike Price (or Exercise Price) of the underlying and the implied volatility of an option are inversely related (Volatility Smile Curve).

In case of a deep in the money call,
Intrinsic Value of Call option = Max (S-X, 0) ;

Here since the option is deep in the money, it means that Stock Price, S is much above the Exercise Price, X. Now since the Exercise price is very low, so the actual implied volatility will be very high (as per the volatility smile curve explained above)

But the risk monitoring system assumes constant volatility for stock’s returns, therefore it will understate the stock’s implied volatility (as the actual volatility as per the volatility smile curve will be very high).

Why can’t the answer be option (c)
Option © is Short position in Deep in the money call
Now, if you are holding a short position in Deep in the money call:
Intrinsic Value of a call option = Max (S-X,0)

A short position in deep in the money call means the holder of the option will be in profit when the Strike price (Exercise Price) will go up and the stock’s price goes down .

Now if Strike price increases, then as per the volatility smile, the implied volatility should go down or decrease.

If the implied volatility decreases, then the risk monitoring system which assumes constant volatility for the stock’s returns will overstate the volatility values. Hence the answer could not be option ©.