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# question 31 on practice exam 2017 - Implied vol

#### Sully MARIE

##### New Member
I am currently preparing the FRM (part 2) and I would need your help on the following question.

A risk manager is in the process of valuing several European-type option positions on a non-dividend-paying stock XYZ that is currently priced at EUR 30. The implied volatility skew, estimated using the Black-Scholes-Merton model and the current prices of actively traded European-style options on stock XYZ at various strike prices, is shown below:

Graph of IV decreasing ... Smirk

Strike Price (EUR)
Assuming that the implied volatility at EUR 30 is used to conduct the valuation, which of the following long positions will be overvalued?
A. An in-the-money call
B. An in-the-money put
C. An out-of-the-money call
D. An out-of-the-money put
Explanation: An out-of-the-money call has a strike price above 30. Therefore, using the chart above, its implied volatility is less than the at-the-money volatility, so using the at-the-money implied volatility would result in pricing an out-of-the-money call option higher than its fair price.

I do understand why C is correct, but I think that In the money put will also be overvalued. Am I right ? Can you please help on this?

#### Nicole Seaman

Staff member
Subscriber
I am currently preparing the FRM (part 2) and I would need your help on the following question.

A risk manager is in the process of valuing several European-type option positions on a non-dividend-paying stock XYZ that is currently priced at EUR 30. The implied volatility skew, estimated using the Black-Scholes-Merton model and the current prices of actively traded European-style options on stock XYZ at various strike prices, is shown below:

Graph of IV decreasing ... Smirk

Strike Price (EUR)
Assuming that the implied volatility at EUR 30 is used to conduct the valuation, which of the following long positions will be overvalued?
A. An in-the-money call
B. An in-the-money put
C. An out-of-the-money call
D. An out-of-the-money put
Explanation: An out-of-the-money call has a strike price above 30. Therefore, using the chart above, its implied volatility is less than the at-the-money volatility, so using the at-the-money implied volatility would result in pricing an out-of-the-money call option higher than its fair price.

I do understand why C is correct, but I think that In the money put will also be overvalued. Am I right ? Can you please help on this?
Hello @Sully MARIE

David discussed this question in the GARP PQ section of our forum. He stated the following, which I think will help to answer your question:

"This is a variation on GARP's 2015 P2 Question #15, link below. Under this equity skew, if we use the ATM implied volatility to price ITM/OTM options then the consistent outcomes would be:
• Strike prices below 30 (to the left) correspond to in-the-money calls and out-of-the-money puts, so that if σ(K=30) is used to value them, ITM calls and OTM puts will be undervalued (because their implied volatility is higher which is driven by a higher price), and similarly
• Strike prices above 30 (to the right) correspond to out-of-the-money calls and in-the-money puts, so that if σ(K=30) is used to value them, OTM calls and ITM puts will be overvalued (because their implied volatility is lower which is driven by a lower price)"

Nicole

#### Sully MARIE

##### New Member
I do understand that OTM calls and ITM puts will be overvalued. However, reading the question, only one option is correct.
So options B (ITM put) should be false since the correct answer is C. Is there an error in the subject ? Are there two correct answers ?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
HI @Sully MARIE Yes, you are absolutely correct! Given the typical equity skew (downward sloping implied vol vs strike price), the higher strike price (to the right on the graph) corresponds equivalently to out-of-the-money (OTM) calls and in the money (ITM) puts, such that, according to your version of the question, both (B) and (C) are true. I don't know what to say, it's very disappointing to me, even years later: this 2017 paper is filled with errors (documented error rate over 30-35%), it's effectively useless as a study aid for candidates. This particular question (garp17-p2-31) has at least three versions issued, as GARP issued corrections. It disappoints me to the extent candidates tend to assume these questions are reliable. My opinion is that you should be careful with prior practice papers, we have submitted a discouraging number of errors. Thanks,

Hi David,