Deck 8: Options

Question 1

A European call option is the:

A)right to buy a unit of the underlying asset at the strike price,at the expiration or exercise date.
B)right to sell a unit of the underlying asset at the strike price,at the expiration or exercise date
C)right to buy a unit of the underlying asset on or before the expiration date of the option.
D)right to sell a unit of the underlying asset on or before the expiration date of the option.

Answer 1

A

Question 2

Which of the following is true of options based on the put-call parity formula?

A)It pays to exercise an American call option prematurely on an equity that pays no dividends before expiration.
B)If the underlying equity pays no dividends before expiration,then the no-arbitrage values of American and European call options with the same features will be different.
C)An investor does not capture the full value of an American call option by exercising between ex-dividend dates.
D)The no-arbitrage prices of American and European call options are the same irrespective of the dividend payments.

Answer 2

C

Question 3

Explain the concept of portfolio insurance.

Answer 3

Portfolio insurance is an option-based investment that,when added to the existing investments of a pension fund or mutual fund,protects the fund's value at a target horizon date against drastic losses.Options have the desirable feature of unlimited upside potential with limited downside risk.Assume a portfolio is composed of a call option,expiring on the future horizon date,with a strike price of K,and riskless zero-coupon bonds worth F,the floor amount,at the option expiration date.The portfolio's value at the date the options expire would never fall below the value of the riskless bonds,the floor amount,at that date.If the underlying asset of the call option performed poorly,the option would expire unexercised; however,because the call option value in this case is zero,the portfolio value would be the value of the riskless bonds.If the underlying asset performed well,the positive value of the call option would enhance the value of the portfolio beyond its floor value.In essence,this portfolio is insured.The present value of the two components of an insured portfolio is (c₀ + PV(F))where c₀ is the value of the call option and PV(F)is the floor amount,discounted at the risk-free rate.

Question 4

Explain the European and American options.

Question 5

Which of the following is true of call and put currency options?

A)If the domestic interest rate is greater than the foreign interest rate,the American option to buy domestic currency in exchange for foreign currency should sell for a price less than that of the European option to do the same.
B)If the domestic interest rate is greater than the foreign interest rate,the American option to buy domestic currency in exchange for foreign currency should sell for a price greater than that of the European option to do the same.
C)If the domestic interest rate is greater than the foreign interest rate,the American option to buy domestic currency in exchange for foreign currency should sell for the same price as the European option to do the same.
D)If the domestic interest rate is same as the foreign interest rate,the American option to buy domestic currency in exchange for foreign currency should sell for the same price as the European option to do the same.

Question 6

Which of the following is true of options?

A)The option writer pays money to the holder to acquire the option.
B)If the exercise price exceeds future share price,the put writer will sell the underlying for more than it is worth.
C)Future cash flows are never positive when writing an option.
D)If the future share price exceeds exercise price,the call writer will buy the underlying for less than its fair value.

Question 7

Under the binomial model,which of the following equations represent the risk-neutral probabilities for the up move? (u = ratio of next period's share price to this period's price if the up state occurs,d = ratio of next period's share price to this period's price if the down state occurs,r_f = risk-free rate.)

A)
B)
C)
D)

Question 8

Which of the following is the correct expression of the Black-Scholes formula?

A)
B)
C)
D)

Question 9

Which of the following is an assumption in the Black-Scholes valuation?

A)Short selling of securities is not permitted in the market.
B)Securities don?t make periodic payments such as for interest or dividends.
C)The logarithm of the return on the underlying equity is normally distributed.
D)Macroeconomic events have no effect on the prices of securities.

Question 10

_____ of an option is the change in the value of the derivative security with respect to movements in the share price,holding everything else constant.

A)Gamma
B)Delta
C)Vega
D)Theta

Question 11

A call option on the equity of a firm is called a compound option because:

A)the value of an option is a function of compound interest.
B)the equity is an option on the assets of the firm.
C)the cash component in the assets is compounded quarterly.
D)the dividends paid are a function of compound interest.

Question 12

Explain why an investor cannot capture the full value of an American call option by exercising between ex-dividend dates.

Question 13

The UK sterling risk-free rate is assumed to be 5.5% per year,and all standard deviations are assumed to be 20% per year.The current spot exchange rate is £0.73/? and the one-year risk-free rate is 3.5% in France.Find the forward price one year from now.

A)£0.7441
B)£0.73
C)£0.7701
D)£0.7556

Question 14

Explain the put-call parity for European options on dividend-paying equities.

Question 15

Which of the following is true of American options?

A)They cannot be exercised before their expiration date.
B)They do not have a strike price but a strike range.
C)Their value is based on the underlying asset?s value.
D)Their exercise commencement date and expiration date are the same.

Question 16

The shares of Zeta Corporation currently sell for €200 and a European call on Zeta has a strike price of €242.The option will expire two years from now and currently sells for €40.Assume the risk-free rate is 12% per year and that the company will certain to pay a dividend of €5 one year from now.Based on the put-call parity formula,find the value of the comparable European put.

A)€35.45
B)€32.92
C)€2.53
D)€37.39

Question 17

Assuming no dividend payments and arbitrage,the put-call parity formula states that a:

A)short position in a call and a long position in a put sells for the current share price plus the strike price discounted at the risk-free rate.
B)short position in a put and a long position in a call sells for the current share price plus the strike price discounted at the risk-free rate.
C)long position in a call and a short position in a put sells for the current share price less the strike price discounted at the risk-free rate.
D)long position in a put and a short position in a call sells for the current share price less the strike price discounted at the risk-free rate.

Question 18

The first term of the Black-Scholes formula, ,is the:

A)annualized standard deviation of the option returns.
B)cost of the shares needed in the tracking portfolio.
C)amount of cash borrowed at the risk-free rate.
D)amount of dividends to be paid in period 1.

Question 19

The expiration value of a put option is _____.(The future price at the expiration date,T,is denoted by S_T and the exercise price is denoted by K )

A)min (0,S_T - K ).
B)max (0,S_T - K ).
C)min (0,K - S_T)
D)max (0,K - S_T)