Question 1

A stock that pays no dividends has a price of $40. If the interest rate is zero, then which if the following statements is valid?

Accepted Answer

A)  The three-month call is worth less than the two-month call. 
B)  The time value of the three-month call is the same as that of the two-month call. 
C)  The insurance value of the three-month call is the same as that of the two-month call. 
D)  The intrinsic value of the three-month call is less than that of the two-month call. 
A)  The three-month call is worth less than the two-month call. 
B)  The time value of the three-month call is the same as that of the two-month call. 
C)  The insurance value of the three-month call is the same as that of the two-month call. 
D)  The intrinsic value of the three-month call is less than that of the two-month call. B

Question 2

Consider two identical European call options on two identical stocks A and B, except that the former stock pays dividends and the latter stock does not. Which of the following statements is most valid?

Accepted Answer

A)  Call A is greater in value than call B. 
B)  The time value of call A is greater than that of call B. 
C)  The time value of call B is greater than that of call A. 
D)  The insurance value of call B is greater than that of call A. 
A)  Call A is greater in value than call B. 
B)  The time value of call A is greater than that of call B. 
C)  The time value of call B is greater than that of call A. 
D)  The insurance value of call B is greater than that of call A. C

Question 3

Given that call prices are convex in strike prices, the implication is that

Accepted Answer

A)  Put prices are concave in strike prices. 
B)  Put prices are linear in strike prices. 
C)  Put prices are convex in strike prices. 
D)  Put prices may be convex or concave in strike prices. 
A)  Put prices are concave in strike prices. 
B)  Put prices are linear in strike prices. 
C)  Put prices are convex in strike prices. 
D)  Put prices may be convex or concave in strike prices. C

Question 4

Consider two six-month American calls at strikes 90 and 100 on a non-dividend paying stock. The risk free rate is 2%. The difference between the two call prices at any time before maturity will always be

Accepted Answer

A)  Less than $10. 
B)  Equal to $10. 
C)  Greater than $10. 
D)  One cannot be sure of which of the preceding three choices is valid and more information may be required. 
A)  Less than $10. 
B)  Equal to $10. 
C)  Greater than $10. 
D)  One cannot be sure of which of the preceding three choices is valid and more information may be required.

Question 5

If you are short a call and long an otherwise identical put on the same stock, where the strike price is the forward price of the stock for the same maturity as the options, you essentially have the following position:

Accepted Answer

A)  A short forward on the stock for the maturity of the option. 
B)  A synthetic collar. 
C)  An options position for which you pay a positive net premium up front. 
D)  An options position for which you receive a net premium up front. 
A)  A short forward on the stock for the maturity of the option. 
B)  A synthetic collar. 
C)  An options position for which you pay a positive net premium up front. 
D)  An options position for which you receive a net premium up front.

Question 6

The stock price is $30. The strike price of a three-month European put option is $32. If the put option is priced at $5, and the risk-free rate of interest is 2%, and the stock pays no dividends, then the insurance value of the option is

Accepted Answer

A)  1.84 
B)  2.00 
C)  3.16 
D)  4.96 
A)  1.84 
B)  2.00 
C)  3.16 
D)  4.96

Question 7

If the interest rate is positive, then which of the following statements is valid for at-the-money call and put options written on the same underlying stock for the same strike and maturity?

Accepted Answer

A)  The call is worth more than the put. 
B)  The call price is equal to the put price. 
C)  The call price is less than the put price. 
D)  More information is needed to determine the relative values of the call and put. 
A)  The call is worth more than the put. 
B)  The call price is equal to the put price. 
C)  The call price is less than the put price. 
D)  More information is needed to determine the relative values of the call and put.

Question 8

An American put option on a stock that pays no dividends:

Accepted Answer

A)  May be exercised early if the stock drops sharply before maturity. 
B)  Is always exercised early when the the put is deep in-the-money, and the volatility of the stock rises sharply from its initial level. 
C)  Is not exercised early unless the growth in the stock is lower than the rate of interest. 
D)  Is never exercised early. 
A)  May be exercised early if the stock drops sharply before maturity. 
B)  Is always exercised early when the the put is deep in-the-money, and the volatility of the stock rises sharply from its initial level. 
C)  Is not exercised early unless the growth in the stock is lower than the rate of interest. 
D)  Is never exercised early.

Question 9

Consider a portfolio comprised of a short call and a short put, both options written on the same stock, same strike, and for the same maturity. Which of the following is valid?

Accepted Answer

A)  The intrinsic value of the portfolio is zero. 
B)  The time value of the portfolio is zero. 
C)  The insurance value of the portfolio is negative. 
D)  All of the above. 
A)  The intrinsic value of the portfolio is zero. 
B)  The time value of the portfolio is zero. 
C)  The insurance value of the portfolio is negative. 
D)  All of the above.

Question 10

For a stock that pays no dividends, which of the following statements is most accurate?

Accepted Answer

A)  Identical American call and put options have the same price. 
B)  An American call has a higher price than an identical American put if the strike price is the forward price of the stock for the maturity of the options. 
C)  An American call has a lower price than an identical American put if the strike price is the forward price of the stock for the maturity of the options. 
D)  Identical American call and put options have the same price if the options are struck at-the-money. 
A)  Identical American call and put options have the same price. 
B)  An American call has a higher price than an identical American put if the strike price is the forward price of the stock for the maturity of the options. 
C)  An American call has a lower price than an identical American put if the strike price is the forward price of the stock for the maturity of the options. 
D)  Identical American call and put options have the same price if the options are struck at-the-money.

Question 11

When an American call has been exercised early, which of the following inferences about the stock and option is valid?

Accepted Answer

A)  The stock must pay dividends after the date of exercise. 
B)  The intrinsic value of the option is positive. 
C)  The time value of the option is negative. 
D)  All of the above. 
A)  The stock must pay dividends after the date of exercise. 
B)  The intrinsic value of the option is positive. 
C)  The time value of the option is negative. 
D)  All of the above.

Question 12

Put-call parity is valid for

Accepted Answer

A)  Stock returns that are normally distributed, that is, stock movements are symmetric, but not otherwise. 
B)  American calls and puts when the stock pays no dividends. 
C)  European calls and puts when the stock pays dividends. 
D)  Stocks but not for currencies. 
A)  Stock returns that are normally distributed, that is, stock movements are symmetric, but not otherwise. 
B)  American calls and puts when the stock pays no dividends. 
C)  European calls and puts when the stock pays dividends. 
D)  Stocks but not for currencies.

Question 13

Consider an American call option and an American put option, on the same dividend-paying stock, both for the same strike and maturity. Which of the following statements is most accurate?

Accepted Answer

A)  Either both options are exercised or neither one is exercised early. 
B)  If the call is exercised early then the put will not be exercised early. 
C)  If the put is exercised early then the call will not be exercised early. 
D)  Both options may be exercised early. 
A)  Either both options are exercised or neither one is exercised early. 
B)  If the call is exercised early then the put will not be exercised early. 
C)  If the put is exercised early then the call will not be exercised early. 
D)  Both options may be exercised early.

Question 14

A stock that pays no dividends has a price of $50. The rate of interest is 10%. The one-month maturity, 60-strike American put is optimally exercised. What can you infer about the insurance value of the option at the time of exercise?

Accepted Answer

A)  The minimum insurance value is $0.62 
B)  The minimum insurance value is $0.50 
C)  The maximum insurance value is $0.41 
D)  The maximum insurance value is $10 
A)  The minimum insurance value is $0.62 
B)  The minimum insurance value is $0.50 
C)  The maximum insurance value is $0.41 
D)  The maximum insurance value is $10

Question 15

A stock that pays no dividends has a price of $50. The one-month maturity, at-the-money European call and put are trading at $10 and $9.90, respectively. The one-month forward price of the stock is:

Accepted Answer

A)  49.90 
B)  50.00 
C)  50.10 
D)  50.20 
A)  49.90 
B)  50.00 
C)  50.10 
D)  50.20

Question 16

The stock price is $50. The strike price of a three-month European put option is $52. If the put option is equal in price to the call option and the stock pays no dividends, then the rate of interest for three month's maturity is

Accepted Answer

A)  4.61% 
B)  9.23% 
C)  12.66% 
D)  15.69% 
A)  4.61% 
B)  9.23% 
C)  12.66% 
D)  15.69%

Question 17

The six-month at-the-money European call option on a stock worth $25 is priced at $5. The rate of interest is 2%. The put is priced at $7. The dividend paid at the end of three months must be

Accepted Answer

A)  1.23 
B)  2.26 
C)  3.83 
D)  4.77 
A)  1.23 
B)  2.26 
C)  3.83 
D)  4.77

Question 18

The stock price is $34. The strike price of a three-month European call option is $32. If the call option is priced at $5, and the risk-free rate of interest is 2%, and the stock pays a dividend of $1 in one month, then the time value of the option is

Accepted Answer

A)  1.16 
B)  2.16 
C)  3.16 
D)  4.16 
A)  1.16 
B)  2.16 
C)  3.16 
D)  4.16

Question 19

An American call option on a stock that pays no dividends:

Accepted Answer

A)  May be exercised early if the stock rises sharply just before maturity. 
B)  Is always exercised early when the the call is deep in-the-money, and the volatility of the stock drops from its initial level. 
C)  Is not exercised early unless the growth in the stock exceeds the rate of interest. 
D)  Is never exercised early. 
A)  May be exercised early if the stock rises sharply just before maturity. 
B)  Is always exercised early when the the call is deep in-the-money, and the volatility of the stock drops from its initial level. 
C)  Is not exercised early unless the growth in the stock exceeds the rate of interest. 
D)  Is never exercised early.

Question 20

An American put option is sometimes exercised early because:

Accepted Answer

A)  The holder of an in-the-money option believes that the stock has bottomed out and expects the stock to rise in the future. 
B)  The absolute time value of the option is larger than the insurance value. 
C)  The volatility of the stock has just increased. 
D)  The skewness of the stock has just increased from its initial level. 
A)  The holder of an in-the-money option believes that the stock has bottomed out and expects the stock to rise in the future. 
B)  The absolute time value of the option is larger than the insurance value. 
C)  The volatility of the stock has just increased. 
D)  The skewness of the stock has just increased from its initial level.

Exam 10: Early-Exercise Put-Call Parity

A stock that pays no dividends has a price of $40. If the interest rate is zero, then which if the following statements is valid?

Consider two identical European call options on two identical stocks A and B, except that the former stock pays dividends and the latter stock does not. Which of the following statements is most valid?

Given that call prices are convex in strike prices, the implication is that

Consider two six-month American calls at strikes 90 and 100 on a non-dividend paying stock. The risk free rate is 2%. The difference between the two call prices at any time before maturity will always be

If you are short a call and long an otherwise identical put on the same stock, where the strike price is the forward price of the stock for the same maturity as the options, you essentially have the following position:

The stock price is $30. The strike price of a three-month European put option is $32. If the put option is priced at $5, and the risk-free rate of interest is 2%, and the stock pays no dividends, then the insurance value of the option is

If the interest rate is positive, then which of the following statements is valid for at-the-money call and put options written on the same underlying stock for the same strike and maturity?

An American put option on a stock that pays no dividends:

Consider a portfolio comprised of a short call and a short put, both options written on the same stock, same strike, and for the same maturity. Which of the following is valid?

For a stock that pays no dividends, which of the following statements is most accurate?

When an American call has been exercised early, which of the following inferences about the stock and option is valid?

Put-call parity is valid for

Consider an American call option and an American put option, on the same dividend-paying stock, both for the same strike and maturity. Which of the following statements is most accurate?

A stock that pays no dividends has a price of $50. The rate of interest is 10%. The one-month maturity, 60-strike American put is optimally exercised. What can you infer about the insurance value of the option at the time of exercise?

A stock that pays no dividends has a price of $50. The one-month maturity, at-the-money European call and put are trading at $10 and $9.90, respectively. The one-month forward price of the stock is:

The stock price is $50. The strike price of a three-month European put option is $52. If the put option is equal in price to the call option and the stock pays no dividends, then the rate of interest for three month's maturity is

The six-month at-the-money European call option on a stock worth $25 is priced at $5. The rate of interest is 2%. The put is priced at $7. The dividend paid at the end of three months must be

The stock price is $34. The strike price of a three-month European call option is $32. If the call option is priced at $5, and the risk-free rate of interest is 2%, and the stock pays a dividend of $1 in one month, then the time value of the option is

An American call option on a stock that pays no dividends:

An American put option is sometimes exercised early because:

Overview

Futures Markets

Pricing Forwards and Futures I

Pricing Forwards Futures II

Hedging With Futures Forwards

Interest-Rate Forwards Futures

Options Markets

Options: Payoffs Trading Strategies

No-Arbitrage Restrictions

Option Pricing: an Introduction

Binomial Option Pricing

Implementing the Binomial Model

The Black-Scholes Model

Mathematics of Black-Scholes

Beyond Black-Scholes

The Option Greeks

Path-Independent Exotic Options

Exotic Options II: Path-Dependent Options

Value at Risk

Swaps and Floating Rate Products

Equity Swaps

Currency and Commodity Swaps

Term Structure of Interest Rates: Concepts

Estimating the Yield Curve

Modeling Term Structure Movements

Factor Models of the Term Structure

The Heath-Jarrow-Morton HJM and Libor Market Model LMM

Credit Derivative Products

Structural Models of Default Risk

Reduced-Form Models of Default Risk

Modeling Correlated Default

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