Baran

 

4、An option dealer is delta hedging a short call position on a stock. As the stock price increases, in order to maintain the hedge, the dealer would most likely have to:

A) buy more shares of the stock. 

B) sell some the shares of the stock.

C) buy T-bills.

D) short T-bills.

Baran

 

The correct answer is A

 

As the value of the underlying increases, the delta of a call option increases. This means more of the underlying asset is needed to hedge the position.

Baran

 

5、To create a delta-neutral portfolio, an investor who has written 5,000 call options that have deltas equal to 0.5 will be:

A) short 2,500 shares in the underlying.

B) long 2,500 shares in the underlying and short 2,500 more options.

C) long 2,500 shares in the underlying.

D) short 2,500 shares in the underlying and be short 2,500 more options.

Baran

 

The correct answer is C

 

If the investor has written 5,000 call options, he then must go long 0.5 × 5,000 = 2,500 shares to create a delta neutral position since the delta of a share is 1.

Baran

 

AIM 4: Compute delta for an option.

 

1、The deltas of puts and calls are most sensitive to changes in the underlying when:

A) both calls and puts are deep in-the-money.

B) both puts and calls are deep out-of-the-money.

C) calls are deep out-of-the-money, but puts are deep in-the-money.

D) both calls and puts are at-the-money.

Baran

 

 The correct answer is D

 

Call and put deltas are the most sensitive to changes in the underlying security (i.e., gammas are largest) when the option is at-the-money.

Baran

 

2、Which of the following is FALSE?

The delta of forwards and futures is 1.

Gamma is largest when options are at-the-money.

Two problems using stop-loss trading on naked options are transaction costs and stock price uncertainty.

For a delta-neutral portfolio, although opposite in sign, theta can serve as a proxy for gamma.

A) II only.

B) I and III only.

C) II and IV only.

D) I only.

Baran

 

 The correct answer is D

 

The delta of forwards is one. The delta of futures is not usually one. Two problems using stop-loss trading on naked options are transaction costs and stock-price certainty. Gamma is largest when options are at-the-money. For a delta-neutral portfolio, although opposite in sign, theta can serve as a proxy for gamma.

Baran

 

The correct answer is A

 

The above diagram is for a long stock, long put strategy (portfolio insurance). The loss is limited to the cost of the option while the potential upside profit is unlimited. Note that the portfolio insurance payoff diagram is identical to the profit/loss diagram for a long call option, however a long call is not one of the answer choices.

Baran

 

AIM 8: Define, compute and discuss theta, gamma, vega, and rho for option positions.

1、Which of the following is the best approximation of the gamma of an option if its delta is equal to 0.6 when the price of the underlying security is 100 and 0.7 when the price of the underlying security is 110?

A) 0.00.

B) 0.01.

C) 0.10.

D) 1.00.