A RISK MANAGER IS IN THE PROCESS OF VALUING SEVERAL EUROPEAN OPTIO...
15.
A risk manager is in the process of valuing several European option positions on a non-dividend-paying stock
XYZ that is currently priced at GBP 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:
Im
p
li
e
d
V
o
la
ti
li
ty
Strike Price (GBP)
Assuming that the implied volatility at GBP 30 is used to conduct the valuation, which of the following long
positions will be undervalued?
a.
An out-of-the-money call
b.
An in-the-money call
c.
An at-the-money put
d.
An in-the-money put
Correct Answer: b
Rationale:
An in-the-money call has a strike price below 30. Therefore, using the chart above, its implied volatility
is greater than the at-the-money volatility, so using the at-the-money implied volatility would result in pricing an
in-the-money call option lower than its fair price.
Section: Market Risk Measurement and Management
Reference:
John Hull, Options, Futures, and Other Derivatives, 9th Edition, Chapter 20, “Volatility Smiles.”
Learning Objective:
Compare the shape of the volatility smile (or skew) to the shape of the implied distribution of
the underlying asset price and to the pricing of options on the underlying asset.
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2015 Financial Risk Manager (FRM®) Practice Exam