Deck 17: The Greek Letters

Question 1

Gamma measures: choose one)

A) The rate of change of delta with the asset price
B) The rate of change of the portfolio value with the passage of time
C) The sensitivity of the portfolio value to interest rate changes
D) None of the above

Answer 1

A

Question 2

A trader uses a stop-loss strategy to hedge a short position in a three-month call option with a strike price of 0.7000 on an exchange rate. The trader covers the option when the exchange rate is 0.7005 and assumes a naked position when the exchange rate is 0.6995. The value of the option is 0.1. Estimate the expected number of times the trader covers the position during the life of the option. _ _ _ _ _ _

Answer 2

100

Question 3

A call option on an asset has a delta of 0.4. A trader has sold 2000 options and wants to create a delta-neutral position.
i) Should the trader take a long or short position in the asset? _ _ _ _ _ _
ii) How many units of the asset should be bought or sold? _ _ _ _ _ _

Answer 3

i): Longii): 800

Question 4

A European call and European put have the same strike price and time to maturity. Which two of the following are true? choose two)

A) The gamma of a call is the same as the gamma of a put.
B) The delta of a call is the same as the delta of a put.
C) The vega of a call is the same as the vega of a put.
D) The theta of a call is the same as the theta of a put.

Question 5

A portfolio of derivatives on a stock has a delta of 2400 and a gamma of -100. An option on the stock with a delta of 0.6 and a gamma of 0.04 can be traded.
i) What position in the option creates a portfolio that is gamma neutral? Give the size of position, and state whether it is long or short. _ _ _ _ _ _
ii) After this position has been taken, what position in the stock is then necessary for delta neutrality? Give the size of position, and state whether it is long or short. _ _ _ _ _ _

Question 6

Vega measures: choose one)

A) The rate of change of delta with the asset price
B) The rate of change of the portfolio value with the passage of time
C) The sensitivity of the portfolio value to interest rate changes
D) None of the above

Question 7

Theta measures: choose one)

A) The rate of change of delta with the asset price
B) The rate of change of the portfolio value with the passage of time
C) The sensitivity of a portfolio value to interest rate changes
D) None of the above