Baran

Which of the following is least accurate regarding the limitations of the BSM model?
A) The BSM is not useful in pricing options on bonds and interest rates.
 
B) The BSM is not useful in situations where the volatility of the underlying asset changes over time. 
 
C) The assumption of no taxes or transaction costs makes the BSM less useful. 
 
D) The BSM is designed to price American options but not European options. 
 

Baran

The  correct answer is D

The following are limitations of the BSM:

1、The assumption of a known and constant risk free rate means the BSM is not useful for pricing options on bond prices and interest rates.
2、The assumption of a known and constant asset return volatility makes the BSM not useful in situations where the volatility is not constant which occurs much of the time.
3、The assumption of no taxes and transaction costs makes the BSM less useful.
4、The BSM is designed to price European options and not American options.  

Baran

If Bingly forecasts the volatility for a stock and find that it is significantly greater than that implied by the prices of the puts and calls of the stock, he would conclude that:
A) puts and calls are overpriced.
 
B) the puts are overpriced and the calls are underpriced.
 
C) puts and calls are underpriced. 

D) the puts are underpriced and the calls are overpriced.   

Baran

The  correct answer is C

There is a positive relationship between the volatility of the stock and the price of both puts and calls. A higher estimate of volatility implies that the prices of both puts and calls should be higher. 

 

Baran

All else being equal, the greater the dividend paid by a stock the:
A) lower the call price and the lower the put price.
 
B) lower the call price and the higher the put price.
 
C) higher the call price and the lower the put price. 
 
D) higher the call price and the higher the put price.

Baran

The  correct answer is B

When dividend payments occur during the life of the option, the price of the underlying stock is reduced (on the ex-dividend date). All else being equal, the lower price reduces the value of call options and increases the value of put options.

Baran

 

9、A two-period interest rate tree has the following expected one-period rates:

The price of a two-period European interest-rate call option on the one-period rate with a strike rate of 6.25% and a principal amount of $100,000 is closest to:

A) $423.89. 

B) $725.86.

C) $449.33.

D) $704.22. 

Baran

 

The  correct answer is A

 

1、Calculate the payoffs on the call in percent for I++ and I+? (= I?+):

   I++ value = (0.0712 ? 0.0625) / 1.0712 = 0.00812173.

   I+? value = (0.0684 ? 0.0625) / 1.0684 = 0.00552228.

   Remember that the payoff on the call value is the present value of the interest rate difference based on the raterealized  at     t= 2 because the payment is received at t = 3.

2、Calculate the t = 1 values (the probabilities in an interest rate tree are 50%):

   At t = 1 the values are I+ = [0.5(0.00812173) + 0.5 (0.00552228)] / 1.0683 = 0.00638585.

   At t = 1 the values are I? = [0.5(0) + 0.5 (0.00552228)] / 1.0617 = 0.00260068.

3、Calculate the t = 0 value:

   At t = 0 the option value is [0.5(0.00638585) + 0.5(0.00260068)] / 1.06 = 0.00423893 0.00423893 × 100,000 = $423.89.

Baran

 

10、Which of the following statements concerning the calculation of value at a node in a binomial interest rate tree is most accurate? The value at each node is the:

A) present value of the two possible values from the next period.

B) sum of the present values of the two possible values from the next period.

C) average of the present values of the two possible values from the next period.

D) average of the future values of the two possible values from the next period.

Baran

 

The correct answer is C

The value at any given node in a binomial tree is the present value of the cash flows at the two possible states immediately to the right of the given node, discounted at the 1-period rate at the node under examination.