Baran

5、Assume that the value of a call option with a strike price of $100 and six months remaining to maturity is $5. For a stock price of $100 and an interest rate of 6 percent, what is the value of the corresponding put option with the same strike price and expiration as the call option?

A) $1.78.
 
B) $2.87.
 
C) $5.00.
 
D) $2.13.

Baran

The  correct answer is D

The formula for put-call parity is: Call – Put = Stock – X/(1+r)t  

Solving for the put results in: Call – Stock + X/(1+r)t = Put 

Rearranging the variables: P = C – S + X/(1+r)t   

Put value = $5 - $100 + $100/1.060.5 = $2.13

Baran

6、Which of the following is the expression for put-call parity (ct = call price, pt = put price, St = stock price (all at time t), X = exercise price of call and put, r = interest rate, T = time at expiration of the options)?

A) St + ct = pt + Xe-r(T-t)
 
 
B) St + pt = ct + Xe-r(T-t)
 
 
C) St + pt = ct - Xe-r(T-t)
 
 
D) St - pt = ct + Xe-r(T-t)

Baran

 The  correct answer is B

Baran

7、A security sells for $40. A 3-month call with a strike of $42 has a premium of $2.49. The risk-free rate is 3 percent. What is the value of the put according to put-call parity?

A) $1.89.
 
B) $3.45.
 
C) $4.18.
 
D) $6.03.

Baran

The  correct answer is C

p = c + Xe–rt – S = 2.49 + 42 e –0.03 × 0.25 – 40 = $4.18

Baran

8、Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic European call option?

A) Buy the stock; sell a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond. 
 
B) Buy the stock; buy a European put option on the same stock with the same exercise price and the same maturity; short an amount equal to the present value of the exercise price worth of a pure-discount riskless bond.
 
C) Sell the stock; buy a European put option on the same stock with the same exercise price and the same maturity; invest an amount equal to the present value of the exercise price in a pure-discount riskless bond.
 
D) Sell the stock; sell a European put option on the same stock with the same exercise price and the same maturity; invest an amount equal to the present value of the exercise price in a pure-discount riskless bond.

Baran

The  correct answer is B

According to put-call parity we can write a European call as: C0 = P0 + S0 – X/(1+Rf)T

We can then read off the right-hand side of the equation to create a synthetic position in the call. We would need to buy the European put, buy the stock, and short or issue a riskless pure-discount bond equal in value to the present value of the exercise price.

Baran

9、Referring to put-call parity, which one of the following alternatives would allow you to create a synthetic stock position?

A) Buy a European call option; buy a European put option; invest the present value of the exercise price in a riskless pure-discount bond. 
 
B) Buy a European call option; short a European put option; invest the present value of the exercise price in a riskless pure-discount bond.
 
C) Sell a European call option; buy a European put option; short the present value of the exercise price worth of a riskless pure-discount bond.
 
D) Sell a European call option; sell a European put option; invest the present value of the exercise price in a riskless pure-discount bond.

Baran

 The  correct answer is B

According to put-call parity we can write a stock position as: S0 = C0 – P0 + X/(1+Rf)T

We can then read off the right-hand side of the equation to create a synthetic position in the stock. We would need to buy the European call, sell the European put, and invest the present value of the exercise price in a riskless pure-discount bond.