[ 2009 FRM Sample Exam ] Market risk measurement and management Q17 management, difficult, following, digital, option

Babul

 

17. A European digital option is due to expire tomorrow. The underlying asset is trading at a price that is very close to the strike of the digital. Which of the following risks does the trader find most difficult to manage?

A. Vega and delta

B. Rho and gamma

C. Delta and gamma

D. In this case, there are no risks that the trader finds difficult to manage

Babul

 

Correct answer is Cfficeffice" />

A is incorrect. Vega of an Option keeps falling as it approaches maturity. With just a day to expire for the European Digital option, Vega will be a negligible amount to be of any worry for the trader.

B is incorrect. Of all the Greeks, ffice:smarttags" />Rho is given the least importance because of the fact that it is typically a small number to have any impact on the Trading Book. Further, short?dated Options Rho is almost negligible. In this case, since the European Digital option is due to expire tomorrow Rho is almost inconsequential.

C is correct. Delta and Gamma are the biggest risks in the book for this trade. Since the Underlying Asset is trading at a price that is very close to the Strike, and because the Option is a Digital, the Payoff from this Option could be either Zero if the Underlying Asset price ends below the Strike (Delta = 0) or it could be the Full Notional if the Underlying Asset price ends above the Strike (Delta = 1).  Delta will fluctuate between 0 and 1 as the Underlying Asset price keeps going above and below the Strike, whereas the Gamma shoots up to a very large number (theoretically Infinite). This makes it a very difficult position for the trader to manage.

D is incorrect. As mentioned above, Delta and Gamma are the biggest risks in this case.

Reference: John C. Hull, Options, Futures and Other Derivatives, 5th Edition ? Chapter 14

Type: Market Risk