Deck 23: Single Period Binomial Heath Jarrow Morton Model

Question 1

Use the following tree to answer the questions that follow.
What are the forward rates f(1,1)in the up and down nodes?

A) 0.0307,0.0402
B) 0.0102,0.0010
C) 0.0102,0.0102
D) 0.0056,0.0056
E) 0.0354,0.0056

Answer 1

A

Question 2

Which of the following statements is correct?

A) The buyer of an interest rate floor earns an amount on each payment date that is equal to the floor rate (or the strike rate)on the contract times the notional.
B) The buyer of an interest rate floor earns an amount on each payment date that has a minimum value equal to the floor rate (or the strike rate)on the contract times the notional.
C) The buyer of an interest rate floor earns profits when interest rates increase,so it is contract that is bullish on interest rates.
D) If the buyer of an interest rate floor issues a floating rate bond that pays bbalibor,then its borrowing cost equals the floor rate (or the strike rate)times the notional.
E) If the buyer of an interest rate floor purchases a floating rate bond that earns bbalibor,then it earns at least the floor rate (or the strike rate)times the notional on each payment date.

Answer 2

E

Question 3

Suppose that a company has issued a floating rate note paying (bbalibor).To create an interest rate collar that confines the payments between 3 percent and 7 percent,the company should trade the following interest rate derivatives:

A) buy a cap with a strike rate of 6.50 percent and sell a floor with a strike rate of 2.50 percent
B) buy a cap with a strike rate of 7.00 percent and sell a floor with a strike rate of 3.00 percent
C) buy a cap with a strike rate of 6.50 percent and sell a floor with a strike rate of 3.50 percent
D) sell a cap with a strike rate of 7.00 percent and buy a floor with a strike rate of 3.00 percent
E) sell a floor with a strike rate of 6.50 percent and buy a floor with a strike rate of 2.50 percent

Answer 3

B

Question 4

Use the following tree to answer the questions that follow.
What are the dollar returns on the one-period zero-coupon bond in the up and down nodes?

A) 1.0307,1.0402
B) 1.0102,1.0010
C) 1.0102,1.0102
D) 1.0056,1.0056
E) 1.0056,1.0402

Question 5

The writer of an interest rate floor contract:

A) has the obligation to buy the underlying bond at a fixed price
B) has the obligation to sell the underlying bond at a fixed price
C) has the obligation to pay (the strike rate minus the spot rate)times the notional
D) has the obligation to pay (the spot rate minus the strike rate)times the notional in case it's a positive number
E) has the obligation to pay (the strike rate minus the spot rate)times the notional in case it's a positive number

Question 6

Which of the following statements is correct?

A) The buyer of an interest rate cap earns an amount on each payment date that is equal to the cap rate (or the strike rate)on the contract times the notional.
B) The buyer of an interest rate cap earns an amount on each payment date that is,at a minimum,the cap rate (or the strike rate)on the contract times the notional.
C) The buyer of an interest rate cap earns profits when interest rates decline,so it is contract that is bearish on interest rates.
D) If the buyer of an interest rate cap borrows using a floating rate bond that pays bbalibor,then its borrowing cost in any period is no larger than the cap rate (or the strike rate of the contract)times the notional.
E) If the buyer of an interest rate cap purchases a floating rate bond that earns bbalibor,then it earns the cap rate (or the strike rate)times the notional each payment date.

Question 7

The following is NOT an assumption underlying the binomial HJM option pricing model:

A) no market frictions
B) no credit risk
C) competitive and well-functioning markets
D) no interest rate uncertainty
E) the forward rates follow a lognormal process

Question 8

Which of the following statements about the binomial interest rate option pricing model is INCORRECT?

A) The binomial model is popular because it is accessible and easy to understand.
B) The binomial model is a useful teaching tool.
C) The binomial model is a versatile model that can price a variety of derivatives.
D) The binomial model illustrates the main tenets of martingale pricing,the key technique that lies at the heart of derivative pricing.
E) The binomial model is more accurate than the Heath-Jarrow-Morton model because it makes a more realistic assumption about the bond price evolution than the HJM model.

Question 9

An interest rate cap is:

A) a European call option on the spot interest rate
B) an American call option on the spot interest rate
C) a portfolio of European call options on the spot interest rate
D) a portfolio of American call options on the spot interest rate
E) a portfolio of European put options on the spot interest rate

Question 10

Assume zero-coupon bond prices are B(0,0)=$1,B(0,1)= $0.967846,B(0,2)=$0.943010.What is the spot rate of interest?

A) 0.0604
B) 0.0332
C) 0.0263
D) 0.0371
E) None of these answers are correct.

Question 11

Which of the following statements about an interest rate cap is correct?

A) For a company that has borrowed using a floating-rate loan,a long position in an interest rate cap prevents interest costs from going above a fixed level.
B) For a company that has purchased a floating-rate loan,a long position in an interest rate cap provides protection against the interest cost going above some fixed level.
C) An interest rate cap guarantees a forward rate that is binding at a future date.
D) An interest rate cap guarantees payments if spot prices move outside an interval,with caps at the top and bottom.
E) None of these answers are correct.

Question 12

The writer of an interest rate cap:

A) has the obligation to sell the underlying bond at a fixed price
B) has the obligation to buy the underlying bond at a fixed price
C) has the obligation to pay (the spot rate minus the strike rate)times the notional
D) has the obligation to pay (the spot rate minus the strike rate)times the notional in case it's a positive number
E) has the obligation to pay (the strike rate minus the spot rate)times the notional in case it's a positive number

Question 13

A necessary and sufficient condition to rule out arbitrage profits in the single-period HJM binomial tree is that the following must hold:

A) "up factor $\gt$ down factor $\gt$ dollar return" [U $\gt$ D $\gt$ (1 + R)] for all zero-coupon bonds
B) U $\gt$ (1 + R) $\gt$ D for all zero-coupon bonds
C) the pseudo-probabilities must be equal for all zero-coupon bond/money market account pairs
D) the pseudo-probabilities must be equal to 1/2
E) None of these answers are correct.

Question 14

An interest rate floor is:

A) a European put option on the spot interest rate
B) an American put option on the spot interest rate
C) a portfolio of European put options on the spot interest rate
D) a portfolio of American put options on the spot interest rate
E) a portfolio of European call options on the spot interest rate

Question 15

Use the following tree to answer the questions that follow.
What are the forward rates f (0,1),f (0,0)?

A) 0.0307,0.0402
B) 0.0102,0.0010
C) 0.0102,0.0102
D) 0.0056,0.0056
E) 0.0354,0.0056

Question 16

Use the fact that the pseudo-probability of default at time zero is (1/ 2)to answer the questions that follow.
Consider a caplet with maturity time 1 and strike price 0.035.What are the payoffs to the option at time 1 in the up and down nodes?

A) 0.0307,0.0402
B) 0.0042,0.0000
C) 0.0354,0.0056
D) 0.0050,0.0050
E) 0.0000,0.0050

Question 17

Assume zero-coupon bond prices are B(0,0)= $1,B(0,1)= $0.967846,B(0,2)= $0.943010.What is the forward rate f (0,1)?

A) 0.0332
B) 0.0375
C) 0.0263
D) 0.0604
E) None of these answers are correct.

Question 18

Use the following tree to answer the questions that follow.
What are the dollar returns on the two-period zero coupon-bond in the up and down nodes?

A) 1.0307,1.0402
B) 1.0102,1.0010
C) 1.0102,1.0102
D) 1.0056,1.0056
E) 1.0354,1.0056

Question 19

Suppose that a portfolio manager has purchased a floating rate bond.To create a zero-cost collar,the manager should trade the following interest rate derivatives that have equal values:

A) sell a cap with a higher strike rate and buy a floor with a lower strike rate
B) buy a cap with a higher strike rate and sell a floor with a lower strike rate
C) sell a floor with a higher strike rate and buy a cap with a lower strike rate
D) buy a floor with a higher strike rate and sell a cap with a lower strike rate
E) None of these answers are correct.

Question 20

Which of the following statements is INCORRECT?

A) Vasicek built one of the first generalized interest rate option pricing models.
B) Spot rate models for valuing interest rate options required the estimation of risk-premium.
C) Spot rate models for valuing interest rate options could not easily match the initial yield curve.
D) The Heath-Jarrow-Morton model is a continuous-time and multifactor model.
E) Black's model,a subcase of the Heath-Jarrow-Morton model,is widely used by traders.

Question 21

Use the fact that the pseudo-probability of default at time zero is (1/ 2)to answer the questions that follow.
Consider a caplet with maturity time 1 and strike price 0.035.What is the time 0 value of the caplet?

A) 0.0025
B) 0.0000
C) 0.0042
D) 0.0050
E) 0.0021

Question 22

Use the fact that the pseudo-probability of default at time zero is (1/ 2)to answer the questions that follow.
Consider a floorlet with maturity time 1 and strike price 0.035.What is the time 0 value of the floorlet?

A) 0.0025
B) 0.0000
C) 0.0042
D) 0.0050
E) 0.0021

Question 23

Use the fact that the pseudo-probability of default at time zero is (1/ 2)to answer the questions that follow.
Consider a floorlet with maturity time 1 and strike price 0.035.What are the payoffs to the option at time 1 in the up and down nodes?

A) 0.0307,0.0402
B) 0.0042,0.0000
C) 0.0354,0.0056
D) 0.0050,0.0050
E) 0.0000,0.0050