Question 1

Option prices are homogeneous of degree one in stock price and strike price.What does this imply?

Accepted Answer

A) That if you double the stock price and the strike price the option price will remain unchanged. 
B) That if you double the stock price the option price will double. 
C) That if you double the stock price and halve the strike price the option price will double 
D) That if you double the stock price and strike price the option price will double. 
A) That if you double the stock price and the strike price the option price will remain unchanged. 
B) That if you double the stock price the option price will double. 
C) That if you double the stock price and halve the strike price the option price will double 
D) That if you double the stock price and strike price the option price will double.

Question 2

Which of the following statements most accurately describes the range of possible values of the delta of a cash-or-nothing call option?

Accepted Answer

A) The delta lies between 0 and $+ 1$
) 
B) The delta lies between $- 1$
And
 $+ 1$
) 
C) The delta is $\geq 0$
) 
D) The delta can take on any value,positive,negative or zero. 
A) The delta lies between 0 and $+ 1$
) 
B) The delta lies between $- 1$
And
 $+ 1$
) 
C) The delta is $\geq 0$
) 
D) The delta can take on any value,positive,negative or zero.

Question 3

A path-independent option is

Accepted Answer

A) An option where the price process is not continuous,i.e. ,it does not follow a smooth path,but jumps from one value to the next. 
B) An option where the option payoff depends on the price of the underlying asset at exercise time but not on the details of the price path followed to that point. 
C) An option where the option payoff is independent of anything that happens to the price of the underlying after inception. 
D) An option where the option payoff is constant regardless of the path taken by the price of the underlying. 
A) An option where the price process is not continuous,i.e. ,it does not follow a smooth path,but jumps from one value to the next. 
B) An option where the option payoff depends on the price of the underlying asset at exercise time but not on the details of the price path followed to that point. 
C) An option where the option payoff is independent of anything that happens to the price of the underlying after inception. 
D) An option where the option payoff is constant regardless of the path taken by the price of the underlying.

Question 4

A compound option is

Accepted Answer

A) An option to compound the option's payoffs at a prespecified rate. 
B) An option based on compounding the price of the underlying at a prespecified rate. 
C) An option on an underlying option. 
D) An option on a compound-interest bearing investment. 
A) An option to compound the option's payoffs at a prespecified rate. 
B) An option based on compounding the price of the underlying at a prespecified rate. 
C) An option on an underlying option. 
D) An option on a compound-interest bearing investment.

Question 5

A US-based investor buys from you a quanto option in which the payoffs from a euro-denominated call on a German company are converted back into US dollars at the fixed rate of $1.25/€.To hedge this transaction

Accepted Answer

A) You must hedge both exchange rate and equity price risk. 
B) You must hedge equity price risk but there is no exchange rate risk. 
C) You must hedge exchange rate risk but there is no equity price risk. 
D) There is nothing you need to do. 
A) You must hedge both exchange rate and equity price risk. 
B) You must hedge equity price risk but there is no exchange rate risk. 
C) You must hedge exchange rate risk but there is no equity price risk. 
D) There is nothing you need to do.

Question 6

A three-month at-the-money call option on a stock index is trading at $5;the index is trading at $50.A forward start option on the index that comes to life in one month,has a life of three months from that point and that will be at-the-money when it comes to life,is trading at $4.98.The one-month rate of interest is 2% in continuously-compounded and annualized terms.What is the one-month forward price of the index?

Accepted Answer

A) $50.00 
B) $50.05 
C) $50.25 
D) $50.45 
A) $50.00 
B) $50.05 
C) $50.25 
D) $50.45

Question 7

Consider the following compound options written on an underlying stock.Which one decreases in value when the stock falls in price?

Accepted Answer

A) A put on a call. 
B) A call on a put. 
C) A put on a put. 
D) None of the above. 
A) A put on a call. 
B) A call on a put. 
C) A put on a put. 
D) None of the above.

Question 8

The delta of a cash-or-nothing binary call option and the gamma of such an option

Accepted Answer

A) is always positive;is always positive. 
B) is always positive;can be positive or negative. 
C) can be positive or negative;is always positive. 
D) can be positive or negative;can be positive or negative. 
A) is always positive;is always positive. 
B) is always positive;can be positive or negative. 
C) can be positive or negative;is always positive. 
D) can be positive or negative;can be positive or negative.

Question 9

You buy an at-the-money chooser option.Immediately after you buy it,the price of the underlying increases very sharply.Other things remaining the same,the value of your chooser likely

Accepted Answer

A) Increases. 
B) Decreases (the put now has no value). 
C) Remains constant (the increase in call value is canceled out by the decrease in put value). 
D) Goes to zero. 
A) Increases. 
B) Decreases (the put now has no value). 
C) Remains constant (the increase in call value is canceled out by the decrease in put value). 
D) Goes to zero.

Question 10

A stock is trading at 100.Consider a two-period binomial model in which the stock price moves up or down each period by factors $u = 1.20$ and $d = 0.80$ ,respectively.Suppose the gross risk-free rate of interest per time-step is 1.04.In this setting,the price of a two-period cash-or-nothing binary put option with a strike of 100 that pays $100 if it finishes in-the-money is

Accepted Answer

A) $36. 
B) $33.28 
C) $64. 
D) $59.17. 
A) $36. 
B) $33.28 
C) $64. 
D) $59.17.

Question 11

Consider a stock that pays no dividends.You hold a portfolio comprising an asset-or-nothing call and a cash-or-nothing put.The options share the same strike,and the cash-or-nothing put pays an amount equal to the strike price if the put finishes in-the-money.Your portfolio is equivalent to

Accepted Answer

A) A vanilla call. 
B) A vanilla put. 
C) A covered call. 
D) A protective put. 
A) A vanilla call. 
B) A vanilla put. 
C) A covered call. 
D) A protective put.

Question 12

At maturity in an asset-or-nothing option written on a stock,

Accepted Answer

A) The holder has a choice of receiving the asset or nothing in exchange for paying the strike price. 
B) The holder receives the stock in exchange for the strike price if the option should finish in-the-money,and nothing otherwise. 
C) The holder receives the stock without paying anything in exchange if the option should finish in-the-money,and nothing otherwise. 
D) The holder receives the stock in exchange for a pre-specified consideration (which could differ from the strike price)if the option should finish in-the-money,and nothing otherwise. 
A) The holder has a choice of receiving the asset or nothing in exchange for paying the strike price. 
B) The holder receives the stock in exchange for the strike price if the option should finish in-the-money,and nothing otherwise. 
C) The holder receives the stock without paying anything in exchange if the option should finish in-the-money,and nothing otherwise. 
D) The holder receives the stock in exchange for a pre-specified consideration (which could differ from the strike price)if the option should finish in-the-money,and nothing otherwise.

Question 13

A quanto option is sometimes called a "wrong-currency" option because the payoffs of the quanto

Accepted Answer

A) Are in a different currency from the premium. 
B) Are computed by converting the payoffs from an underlying option in a foreign currency option back to the home currency at a pre-specified exchange rate that may be unrelated to the actual exchange rate. 
C) Are in a different currency from the investor's home currency. 
D) Are computed by converting the payoffs from an underlying home-currency option into a foreign currency at the current exchange rate. 
A) Are in a different currency from the premium. 
B) Are computed by converting the payoffs from an underlying option in a foreign currency option back to the home currency at a pre-specified exchange rate that may be unrelated to the actual exchange rate. 
C) Are in a different currency from the investor's home currency. 
D) Are computed by converting the payoffs from an underlying home-currency option into a foreign currency at the current exchange rate.

Question 14

You have written a put on a put,where the underlying put is written on a stock index.To delta hedge yourself you can either go the underlying put or the underlying index.

Accepted Answer

A) short;short. 
B) short;long. 
C) long;short. 
D) long;long. 
A) short;short. 
B) short;long. 
C) long;short. 
D) long;long.

Question 15

You are long a portfolio of vanilla call options.Which of the following will help you hedge away your theta risk?

Accepted Answer

A) Buying a portfolio of in-the-money cash-or-nothing call options. 
B) Buying a portfolio of out-of-the money cash-or-nothing call options. 
C) Buying a portfolio of in-the-money vanilla call options. 
D) Buying a portfolio of out-of-the money vanilla call options. 
A) Buying a portfolio of in-the-money cash-or-nothing call options. 
B) Buying a portfolio of out-of-the money cash-or-nothing call options. 
C) Buying a portfolio of in-the-money vanilla call options. 
D) Buying a portfolio of out-of-the money vanilla call options.

Question 16

A forward-start option may be viewed as path-independent because

Accepted Answer

A) The features of the option when it comes to life depend on the price of the underlying at that point but not on the path taken to reach that price. 
B) The payoff of the forward-start on its maturity date does not depend on any features of the price path of the underlying from the date of purchase of the option. 
C) A forward start option always starts irrespective of the path taken to the forward start date. 
D) Only the strike price of the option is unknown at the time of entering into the option. 
A) The features of the option when it comes to life depend on the price of the underlying at that point but not on the path taken to reach that price. 
B) The payoff of the forward-start on its maturity date does not depend on any features of the price path of the underlying from the date of purchase of the option. 
C) A forward start option always starts irrespective of the path taken to the forward start date. 
D) Only the strike price of the option is unknown at the time of entering into the option.

Question 17

In comparing a chooser to its straddle counterpart,which of the following statements is not valid?

Accepted Answer

A) A straddle is always worth more than chooser. 
B) The delta of a straddle is always greater than that of a chooser. 
C) The delta of a chooser lies between $- 1$
And
 $+ 1$
) 
D) The delta of a straddle lies between $- 1$
And
 $+ 1$
) 
A) A straddle is always worth more than chooser. 
B) The delta of a straddle is always greater than that of a chooser. 
C) The delta of a chooser lies between $- 1$
And
 $+ 1$
) 
D) The delta of a straddle lies between $- 1$
And
 $+ 1$
)

Question 18

The gamma of a cash-or-nothing binary call option is generally when the option is out-of-the-money and generally when it is in-the-money.

Accepted Answer

A) negative;positive. 
B) negative;negative. 
C) positive;negative. 
D) positive;positive. 
A) negative;positive. 
B) negative;negative. 
C) positive;negative. 
D) positive;positive.

Question 19

A stock is trading at 100.Consider a two-period binomial model in which the stock price moves up or down each period by factors $u = 1.20$ and $d = 0.80$ ,respectively.The gross risk-free rate of interest per time step is 1.04.You are long a cash-or-nothing digital call option that pays $100 if $S _ { T } \geq 100$ ,and nothing otherwise;and short a cash-or-nothing digital put option that pays $100 if $S _ { T } \leq 100$ ,and nothing otherwise.(Here, $S _ { T }$ is the stock price at the end of two periods. )The value of your portfolio is

Accepted Answer

A) Positive. 
B) zero. 
C) Negative. 
D) Cannot be calculated from the given information. 
A) Positive. 
B) zero. 
C) Negative. 
D) Cannot be calculated from the given information.

Question 20

As maturity approaches,the delta of an at-the-money cash-or-nothing digital call option

Accepted Answer

A) Increases. 
B) Decreases. 
C) Remains constant. 
D) Converges to a value of $1 / 2$
) 
A) Increases. 
B) Decreases. 
C) Remains constant. 
D) Converges to a value of $1 / 2$
)

Exam 18: Path-Independent Exotic Options

Option prices are homogeneous of degree one in stock price and strike price.What does this imply?

Which of the following statements most accurately describes the range of possible values of the delta of a cash-or-nothing call option?

A path-independent option is

A compound option is

A US-based investor buys from you a quanto option in which the payoffs from a euro-denominated call on a German company are converted back into US dollars at the fixed rate of $1.25/€.To hedge this transaction

Consider the following compound options written on an underlying stock.Which one decreases in value when the stock falls in price?

The delta of a cash-or-nothing binary call option and the gamma of such an option

You buy an at-the-money chooser option.Immediately after you buy it,the price of the underlying increases very sharply.Other things remaining the same,the value of your chooser likely

Consider a stock that pays no dividends.You hold a portfolio comprising an asset-or-nothing call and a cash-or-nothing put.The options share the same strike,and the cash-or-nothing put pays an amount equal to the strike price if the put finishes in-the-money.Your portfolio is equivalent to

At maturity in an asset-or-nothing option written on a stock,

A quanto option is sometimes called a "wrong-currency" option because the payoffs of the quanto

You have written a put on a put,where the underlying put is written on a stock index.To delta hedge yourself you can either go the underlying put or the underlying index.

You are long a portfolio of vanilla call options.Which of the following will help you hedge away your theta risk?

A forward-start option may be viewed as path-independent because

In comparing a chooser to its straddle counterpart,which of the following statements is not valid?

The gamma of a cash-or-nothing binary call option is generally when the option is out-of-the-money and generally when it is in-the-money.

As maturity approaches,the delta of an at-the-money cash-or-nothing digital call option

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

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 Hjmand 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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