Question 1

The delta of a up-and-out call option with barrier $H$ lying above the strike $K$ is most likely to be negative when

Accepted Answer

A)  The underlying stock price $S$ is at or near $K$ . 
B)  The underlying stock price $S$ is close to and less than $H$ . 
C)  The underlying stock price $S$ is well below $K$ . 
D)  The delta of a call cannot be negative. 
A)  The underlying stock price $S$ is at or near $K$ . 
B)  The underlying stock price $S$ is close to and less than $H$ . 
C)  The underlying stock price $S$ is well below $K$ . 
D)  The delta of a call cannot be negative. B

Question 2

You hold a fixed-strike lookback put option written on a stock that was at-the-money at inception. The stock price at inception was $56, the stock price at maturity is $63, and the lowest and highest stock prices observed over the option's life are, respectively, $52 and $64. The payoff from the option at maturity is

Accepted Answer

A)  Zero. 
B)  $4. 
C)  $8. 
D)  $11. 
A)  Zero. 
B)  $4. 
C)  $8. 
D)  $11. B

Question 3

Which of the following statements is most valid?

Accepted Answer

A)  Asian options are useful for hedging risk to markets in Asia. 
B)  Asian options are usually more expensive than vanilla options because they are exotic. 
C)  Asian options are useful for hedging exposure to the average price of a security or commodity. 
D)  Asian options are more sensitive to volatility than vanilla options. 
A)  Asian options are useful for hedging risk to markets in Asia. 
B)  Asian options are usually more expensive than vanilla options because they are exotic. 
C)  Asian options are useful for hedging exposure to the average price of a security or commodity. 
D)  Asian options are more sensitive to volatility than vanilla options. C

Question 4

Consider a down-and-out call and a down-and-in call with a current stock price $S$ , barrier $H  H$ . When does the knock-out option increase in price and the knock-in decrease in price?

Accepted Answer

A)  When the stock price increases. 
B)  When the volatility increases. 
C)  When the barrier increases. 
D)  When the strike increases. 
A)  When the stock price increases. 
B)  When the volatility increases. 
C)  When the barrier increases. 
D)  When the strike increases.

Question 5

When volatility increases, the value of a down-and-out put , and the value of a down-and-in put.

Accepted Answer

A)  increases; increases. 
B)  decreases; increases. 
C)  may increase or decrease; increases. 
D)  decreases; may increase or decrease. 
A)  increases; increases. 
B)  decreases; increases. 
C)  may increase or decrease; increases. 
D)  decreases; may increase or decrease.

Question 6

A number of companies were accused of "backdating" executive stock options in the 2000s. Backdating is the procedure by which companies chose the date on which the stock was was most favorable (i.e., at its lowest) to act as the putative start date of the option grant. By permitting backdating, companies were essentially giving their executives a form of a

Accepted Answer

A)  Cliquet option. 
B)  Shout option. 
C)  Floating-strike lookback option. 
D)  Fixed-strike lookback option. 
A)  Cliquet option. 
B)  Shout option. 
C)  Floating-strike lookback option. 
D)  Fixed-strike lookback option.

Question 7

When is an Asian option less useful than a vanilla option?

Accepted Answer

A)  For reducing the incentives for price manipulation of the underlying close to maturity. 
B)  For making the option less sensitive to jump risk close to maturity. 
C)  For hedging exposure to the average price of a security. 
D)  For taking directional bets. 
A)  For reducing the incentives for price manipulation of the underlying close to maturity. 
B)  For making the option less sensitive to jump risk close to maturity. 
C)  For hedging exposure to the average price of a security. 
D)  For taking directional bets.

Question 8

If you buy a knock-out call option with barrier $H$ satisfying $H > K = S$ where $K$ and $S$ are the strike price and current price of the underlying, respectively, then your implied view of prices is that

Accepted Answer

A)  Prices are going up to at least the level of the barrier. 
B)  Prices are going up, but at most to the level of the barrier. 
C)  Prices are moving down. 
D)  Prices may move up to the level of the barrier before moving down. 
A)  Prices are going up to at least the level of the barrier. 
B)  Prices are going up, but at most to the level of the barrier. 
C)  Prices are moving down. 
D)  Prices may move up to the level of the barrier before moving down.

Question 9

You hold a floating-strike lookback put option written on a stock. The stock price at inception was $56, the stock price at maturity is $63, and the lowest and highest stock prices observed over the option's life are, respectively, $52 and $64. The payoff from the option at maturity is

Accepted Answer

A)  Zero. 
B)  $1. 
C)  $11 
D)  Cannot be answered without information on the strike price. 
A)  Zero. 
B)  $1. 
C)  $11 
D)  Cannot be answered without information on the strike price.

Question 10

The most valid relationship between the values of European calls ( $C _ { E }$ ), American calls ( $C _ { A }$ ), shout call options ( $C _ { S }$ ), and lookback calls ( $C _ { L }$ ) is as follows:

Accepted Answer

A)  $C _ { A } \leq C _ { S } \leq C _ { L }$ 
B)  $C _ { E } \leq C _ { L } \leq C _ { S }$ 
C)  $C _ { S } \leq C _ { E } \leq C _ { A }$ 
D)  $C _ { A } \leq C _ { L } \leq C _ { S }$ 
A)  $C _ { A } \leq C _ { S } \leq C _ { L }$ 
B)  $C _ { E } \leq C _ { L } \leq C _ { S }$ 
C)  $C _ { S } \leq C _ { E } \leq C _ { A }$ 
D)  $C _ { A } \leq C _ { L } \leq C _ { S }$

Question 11

An option is said to be path-dependent if

Accepted Answer

A)  It has a payoff that depends in some way on the path of prices taken by the underlying. 
B)  It can only be priced on a non-recombining tree. 
C)  Different paths of the asset price necessarily lead to different payoffs. 
D)  All of the above. 
A)  It has a payoff that depends in some way on the path of prices taken by the underlying. 
B)  It can only be priced on a non-recombining tree. 
C)  Different paths of the asset price necessarily lead to different payoffs. 
D)  All of the above.

Question 12

In one type of a lookback option,

Accepted Answer

A)  You can decide to change the option from a call to a put or vice versa at the last minute. 
B)  You can take any observed price prior to maturity as the strike of the option. 
C)  You can take the average observed price of the underlying in determining the option payoff. 
D)  The initial price of the underlying acts as the strike price of the option. 
A)  You can decide to change the option from a call to a put or vice versa at the last minute. 
B)  You can take any observed price prior to maturity as the strike of the option. 
C)  You can take the average observed price of the underlying in determining the option payoff. 
D)  The initial price of the underlying acts as the strike price of the option.

Question 13

Cliquet options are purchased because

Accepted Answer

A)  A portfolio of forward start options is cheaper than buying them separately. 
B)  There is diversification in a portfolio of forward start options. 
C)  They are analogous to owning Asian forward options. 
D)  It is the same as buying rolling forward start options but has the advantage of locking in possibly low volatilities today. 
A)  A portfolio of forward start options is cheaper than buying them separately. 
B)  There is diversification in a portfolio of forward start options. 
C)  They are analogous to owning Asian forward options. 
D)  It is the same as buying rolling forward start options but has the advantage of locking in possibly low volatilities today.

Question 14

Consider a floating-strike lookback put option written on a stock. Let $S ^ { \max }$ and $S ^ { \min }$ denote the maximum and minimum prices of the stock over the option's life. Then, the payoff to the option holder is given by $\max \{ X - Y , 0 \}$ , where

Accepted Answer

A)  $X = S ^ { \max }$ and $Y = K$ , the given strike price of the option. 
B)  $X = K$ and $Y = S ^ { \min }$ . 
C)  $X = S ^ { \max }$ and $Y = S _ { T }$ , the price of the underlying at maturity. 
D)  $X = S _ { T }$ and $Y = S ^ { \min }$ . 
A)  $X = S ^ { \max }$ and $Y = K$ , the given strike price of the option. 
B)  $X = K$ and $Y = S ^ { \min }$ . 
C)  $X = S ^ { \max }$ and $Y = S _ { T }$ , the price of the underlying at maturity. 
D)  $X = S _ { T }$ and $Y = S ^ { \min }$ .

Question 15

A number of companies were accused of "backdating" executive stock options in the 2000s. Backdating is the procedure by which companies chose the date on which the stock was was most favorable (i.e., at its lowest) to act as the putative start date of the option grant. By permitting backdating, companies were essentially giving their executives a form of a

Accepted Answer

A)  Cliquet option. 
B)  Shout option. 
C)  Floating-strike lookback option. 
D)  Fixed-strike lookback option. 
A)  Cliquet option. 
B)  Shout option. 
C)  Floating-strike lookback option. 
D)  Fixed-strike lookback option.

Question 16

In a barrier option,

Accepted Answer

A)  Price paths are bounced off the barrier. 
B)  Option payoffs are conditional on whether the underlying breached the barrier during the option's life. 
C)  Option payoffs are conditional on when the underlying breached the barrier during the option's life. 
D)  Conditional on the barrier being breached during the option's life, option payoffs differ based on how many times the barrier was breached. 
A)  Price paths are bounced off the barrier. 
B)  Option payoffs are conditional on whether the underlying breached the barrier during the option's life. 
C)  Option payoffs are conditional on when the underlying breached the barrier during the option's life. 
D)  Conditional on the barrier being breached during the option's life, option payoffs differ based on how many times the barrier was breached.

Question 17

Which of the following statements is FALSE?

Accepted Answer

A)  Asian calls are always worth less than the corresponding vanilla calls. 
B)  Asian puts are always worth less than the corresponding vanilla puts. 
C)  Arithmetic-average Asian calls are always worth less than the corresponding vanilla calls but geometric-average Asian calls may be worth more. 
D)  At low volatilities, all Asian options are worth less than the corresponding vanilla options, but at high volatilities they may be worth more. 
A)  Asian calls are always worth less than the corresponding vanilla calls. 
B)  Asian puts are always worth less than the corresponding vanilla puts. 
C)  Arithmetic-average Asian calls are always worth less than the corresponding vanilla calls but geometric-average Asian calls may be worth more. 
D)  At low volatilities, all Asian options are worth less than the corresponding vanilla options, but at high volatilities they may be worth more.

Question 18

Consider two paths A and B for stock prices in a barrier option setting that result in the same terminal price. Paths A and B will have different payoff consequences for the barrier option if

Accepted Answer

A)  Path A crossed the barrier before maturity while Path B did not. 
B)  Both paths crossed the barrier prior to maturity but Path A re-crossed it while Path B did not. 
C)  Neither path crossed the barrier prior to maturity. 
D)  All of the above. 
A)  Path A crossed the barrier before maturity while Path B did not. 
B)  Both paths crossed the barrier prior to maturity but Path A re-crossed it while Path B did not. 
C)  Neither path crossed the barrier prior to maturity. 
D)  All of the above.

Question 19

A cliquet is equivalent to a family of forward starting options in which one option comes to life at each reset date and expires on the next reset date. A reverse cliquet

Accepted Answer

A)  Is a portfolio of vanilla put options, all at-the-money today, and expiring on the reset dates of the reverse cliquet. 
B)  Is a portfolio of digital put options, with one option coming to life at each reset date and expiring at the next reset date. 
C)  Is a cliquet that runs in reverse, with options expiring at each reset date whose strike is determined only at the next reset date. 
D)  Has an identical structure to the cliquet but in which there is a promised fixed return at expiry that is reduced by the moneyness at expiry of each forward starting option in the cliquet. 
A)  Is a portfolio of vanilla put options, all at-the-money today, and expiring on the reset dates of the reverse cliquet. 
B)  Is a portfolio of digital put options, with one option coming to life at each reset date and expiring at the next reset date. 
C)  Is a cliquet that runs in reverse, with options expiring at each reset date whose strike is determined only at the next reset date. 
D)  Has an identical structure to the cliquet but in which there is a promised fixed return at expiry that is reduced by the moneyness at expiry of each forward starting option in the cliquet.

Question 20

Consider an option that pays $1000 if the stock price at maturity falls outside a range $\left[ K _ { 1 } , K _ { 2 } \right]$ . Which of the following is valid?

Accepted Answer

A)  The option may be written as the sum of two barrier options. 
B)  The option decreases in value as $K _ { 2 } - K _ { 1 }$ decreases. 
C)  The option may be written as the sum of two asset-or-nothing options. 
D)  The option may be written as the sum of two cash-or-nothing options. 
A)  The option may be written as the sum of two barrier options. 
B)  The option decreases in value as $K _ { 2 } - K _ { 1 }$ decreases. 
C)  The option may be written as the sum of two asset-or-nothing options. 
D)  The option may be written as the sum of two cash-or-nothing options.

Exam 19: Exotic Options II: Path-Dependent Options

The delta of a up-and-out call option with barrier HHH lying above the strike KKK is most likely to be negative when

Which of the following statements is most valid?

Consider a down-and-out call and a down-and-in call with a current stock price SSS , barrier H<SH < SH<S , and strike K>HK > HK>H . When does the knock-out option increase in price and the knock-in decrease in price?

When volatility increases, the value of a down-and-out put , and the value of a down-and-in put.

When is an Asian option less useful than a vanilla option?

If you buy a knock-out call option with barrier HHH satisfying H>K=SH > K = SH>K=S where KKK and SSS are the strike price and current price of the underlying, respectively, then your implied view of prices is that

You hold a floating-strike lookback put option written on a stock. The stock price at inception was $56, the stock price at maturity is $63, and the lowest and highest stock prices observed over the option's life are, respectively, $52 and $64. The payoff from the option at maturity is

The most valid relationship between the values of European calls ( CEC _ { E }CE​ ), American calls ( CAC _ { A }CA​ ), shout call options ( CSC _ { S }CS​ ), and lookback calls ( CLC _ { L }CL​ ) is as follows:

An option is said to be path-dependent if

In one type of a lookback option,

Cliquet options are purchased because

In a barrier option,

Which of the following statements is FALSE?

Consider two paths A and B for stock prices in a barrier option setting that result in the same terminal price. Paths A and B will have different payoff consequences for the barrier option if

A cliquet is equivalent to a family of forward starting options in which one option comes to life at each reset date and expires on the next reset date. A reverse cliquet

Consider an option that pays $1000 if the stock price at maturity falls outside a range [K1,K2]\left[ K _ { 1 } , K _ { 2 } \right][K1​,K2​] . Which of the following is valid?

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

Early-Exercise Put-Call Parity

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

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

Filters

The delta of a up-and-out call option with barrier $H$ lying above the strike $K$ is most likely to be negative when

Consider a down-and-out call and a down-and-in call with a current stock price $S$ , barrier $H < S$ , and strike $K > H$ . When does the knock-out option increase in price and the knock-in decrease in price?

If you buy a knock-out call option with barrier $H$ satisfying $H > K = S$ where $K$ and $S$ are the strike price and current price of the underlying, respectively, then your implied view of prices is that

The most valid relationship between the values of European calls ( $C _ { E }$ ), American calls ( $C _ { A }$ ), shout call options ( $C _ { S }$ ), and lookback calls ( $C _ { L }$ ) is as follows:

Consider an option that pays $1000 if the stock price at maturity falls outside a range $\left[ K _ { 1 } , K _ { 2 } \right]$ . Which of the following is valid?