Question 1

What is the boundary condition for a European put option?

Accepted Answer

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

Question 2

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?

Accepted Answer

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

Question 3

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

Accepted Answer

A firm has income in yen from overseas operations that may be valued in dollars.

Question 4

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?

Accepted Answer

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

Question 5

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?

Accepted Answer

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

Question 6

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?

Accepted Answer

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

Question 7

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?

Accepted Answer

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

Question 8

How does a dividend payment impact the option price?

Accepted Answer

The stock price represents the

Question 9

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

Accepted Answer

At lower strike pric

Question 10

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?

Accepted Answer

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

Question 11

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?

Accepted Answer

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

Question 12

What is the boundary condition for a European call option?

Accepted Answer

A)  Max [0,S(T)-K] 
B)  Max [0,K-S(T)] 
C)  Min [0,S(T)-K] 
D)  Min [0,K-S(T)] 
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 13

Which of the following equations represents a call power option?

Accepted Answer

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

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?

Accepted Answer

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

Question 15

Briefly define a terminal boundary condition.

Accepted Answer

European options fall into thi

Question 16

Which of the following examples does not involve different numeraire?

Accepted Answer

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

Question 17

Define a power option.

Accepted Answer

An option whose payoff,at matu

Question 18

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?

Accepted Answer

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

Question 19

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.

Accepted Answer

The Black-Scholes equation is a mathemat

Exam 21: The Black-Scholes-Merton Equation

What is the boundary condition for a European put option?

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

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?

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?

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?

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?

How does a dividend payment impact the option price?

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

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?

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?

What is the boundary condition for a European call option?

Which of the following equations represents a call power option?

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?

Briefly define a terminal boundary condition.

Which of the following examples does not involve different numeraire?

Define a power option.

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.

Introduction to Derivatives

An Introduction to Forwards and Options

Insurance, collars, and Other Strategies

Introduction to Risk Management

Financial Forwards and Futures

Commodity Forwards and Futures

Interest Rate Forwards and Futures

Swaps

Parity and Other Option Relationships

Binomial Option Pricing: Basic Concepts

Binomial Option Pricing: Selected Topics

The Black-Scholes Formula

Market-Making and Delta-Hedging

Exotic Options: I

Financial Engineering and Security Design

Corporate Applications

Real Options

The Lognormal Distribution

Monte Carlo Valuation

Brownian Motion and Itos Lemma

Risk-Neutral and Martingale Pricing

Exotic Options: 2

Volatility

Interest Rate and Bond Derivatives

Value at Risk

Credit Risk

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