Deck 21: The Black-Scholes-Merton Equation

Question 1

What term is sometimes used to describe the price at a particular point in time,say maturity,that is necessary to calculate today's price?

A) Face value
B) Par value
C) Boundary condition
D) All of the above

Answer 1

D

Question 2

How does a dividend payment impact the option price?

Answer 2

The stock price represents the present value of future dividends,thus,in essence,modifies the return and will adjust the option price.

Question 3

Assume S = $48.35,K = 45,σ = 0.23,r = 0.04,T - t = 60 days,div = 0,and a jump probability = 0.005.What is the increase in the value of a call over a no-jump call?

A) $0.04
B) $0.03
C) $0.02
D) $0.01

Answer 3

B

Question 4

What do we call an option in which the holder has a claim that pays one share of stock if ?S(T)> K,and nothing otherwise?

A) Cash-or-nothing option
B) Asset-or-nothing option
C) Exotic option
D) Digital cash

Question 5

Define a power option.

Question 6

Which of the following equations represents a call power option?

A) Min (Kᵃ-Sᵃ,0)
B) Max (Kᵃ-Sᵃ,0)
C) Min (Sᵃ-Kᵃ,0)
D) Max (Sᵃ-Kᵃ,0)

Question 7

Assume S = $60,K = $65,σ = 0.15,r = 0.05,T - t = 122 days,div = 0.015,and a jump probability = 0.003.What is the value of a call?

A) $0.67
B) $1.67
C) $2.67
D) $3.67

Question 8

Lapel Inc.stock price is $32.00.Joe bets Sarah that the price will be above $35.00 in 6 months (180 days).The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%.If Joe wins the bet,he wishes to be paid with one share of stock.What is the value of the wager to Joe?

A) $3.00
B) $9.65
C) $12.44
D) $19.58

Question 9

Briefly define a terminal boundary condition.

Question 10

Which of the following examples does not involve different numeraire?

A) Currency translation
B) Quantity uncertain
C) Backward equation
D) All-or-nothing options

Question 11

How does the Black-Scholes equation explain the pricing of derivatives? Ask the class to explain the variety of ways in which the Black-Scholes model can be modified in order to price various derivatives.

Question 12

Explain the relationship between strike prices and implied volatilities under a price jump scenario.

Question 13

Lapel Inc.stock price is $32.00.Joe bets Sarah that the price will be above $35.00 in 6 months (180 days).The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%.If Joe wins the bet,he wishes to be paid with one share of stock.If Sarah agrees to the bet,what is the value of her wager?

A) $3.00
B) $9.65
C) $12.44
D) $19.58

Question 14

Assume S = $52.50,K = $55,σ = 0.20,r = 0.045,T - t = 130 days,div = 0.01,and a jump probability = 0.007.What is the value of a put option?

A) $3.63
B) $2.63
C) $1.63
D) $0.63

Question 15

Lapel Inc.stock price is $32.00.Joe bets Sarah that the price will be above $35.00 in 6 months (180 days).The standard deviation of the stock is 0.25 and the risk free interest rate is 5.0%.If Joe wins the bet,he wishes to be paid with one share of stock.At approximately what stock price will the wager be of equal value to both Joe and Sarah?

A) $32.00
B) $33.30
C) $34.25
D) $35.00

Question 16

Mary wagers to pay one share of stock to Matt if the price at expiration in 1 year is above $75.00.Assume S(0)= 60.00,σ = 0.15,r = 0.04,and dividend rate = 0.01.What is the value of Mary's bet?

A) $6.55
B) $7.55
C) $8.55
D) $9.55

Question 17

What is the boundary condition for a European call option?

A) Max [0,S(T)-K]
B) Max [0,K-S(T)]
C) Min [0,S(T)-K]
D) Min [0,K-S(T)]

Question 18

Give an example of currency translation that is a change in numeraire.

Question 19

What is the boundary condition for a European put option?

A) Max [0,S(T)-K]
B) Max [0,K-S(T)]
C) Min [0,S(T)-K]
D) Min [0,K-S(T)]