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 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

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 B

A portfolio of the three instruments will have the identical profit and loss pattern as the fourth instrument and therefore the same value by no arbitrage. So the fourth security can be synthetically replicated using the remaining three.

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.