Question 1

The risk-neutral pricing of options

Accepted Answer

A) Assumes investors are neutral to risk. 
B) Assumes some investors are risk-neutral and others risk-loving,but on average they are neutral to risk. 
C) Is a no-arbitrage pricing approach. 
D) Is valid only in a world with risk-neutral investors and not in the real world. 
A) Assumes investors are neutral to risk. 
B) Assumes some investors are risk-neutral and others risk-loving,but on average they are neutral to risk. 
C) Is a no-arbitrage pricing approach. 
D) Is valid only in a world with risk-neutral investors and not in the real world. C

Question 2

The current price of a stock is 40.After one period,it will be worth either 41.80 or 38.20 with probabilities 0.60 and 0.40,respectively.The risk-free rate of interest over this period,in gross terms,is 1.05 (i.e. ,a dollar invested at the beginning of the period returns 1.05 at the end of the period).The no-arbitrage value of a one-period call option on this stock with a strike of 40

Accepted Answer

A) is approximately 1.03. 
B) is approximately 1.81. 
C) can be anything between 0 and 1.80. 
D) does not exist in the given setting. 
A) is approximately 1.03. 
B) is approximately 1.81. 
C) can be anything between 0 and 1.80. 
D) does not exist in the given setting. D

Question 3

"Portfolio insurance" refers to a trading strategy in which

Accepted Answer

A) You insure a portfolio of bonds against default at the aggregate level rather than buying insurance on each separate bond. 
B) You insure a portfolio of bonds against default by buying an insurance policy that pays a fixed sum of money if a trigger number of defaults occurs. 
C) You look to create a synthetic put on a given portfolio by dynamically trading in the assets in the portfolio. 
D) You insure a portfolio of stocks against a fall in their value by buying an insurance policy that pays a fixed sum of money if your portfolio value falls below a trigger level. 
A) You insure a portfolio of bonds against default at the aggregate level rather than buying insurance on each separate bond. 
B) You insure a portfolio of bonds against default by buying an insurance policy that pays a fixed sum of money if a trigger number of defaults occurs. 
C) You look to create a synthetic put on a given portfolio by dynamically trading in the assets in the portfolio. 
D) You insure a portfolio of stocks against a fall in their value by buying an insurance policy that pays a fixed sum of money if your portfolio value falls below a trigger level. C

Question 4

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If an investment of a dollar at the risk-free rate returns $1.001668 after one month,what is the price of an Arrow security in the state where the stock price moves up?

Accepted Answer

A) 0.4974 
B) 0.4983 
C) 0.5000 
D) 0.5075 
A) 0.4974 
B) 0.4983 
C) 0.5000 
D) 0.5075

Question 5

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-neutral probability of the stock going up is equal to 0.52,what is the price of a one-month call option at a strike price of $102?

Accepted Answer

A) $2.84 
B) $3.14 
C) $3.84 
D) $4.14 
A) $2.84 
B) $3.14 
C) $3.84 
D) $4.14

Question 6

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If an investment of a dollar at the risk-free rate returns $1.001668 after one month,what is the standard deviation of monthly stock return under the risk-neutral probabilities?

Accepted Answer

A) 9.93% 
B) 9.97% 
C) 10.00% 
D) 20.00% 
A) 9.93% 
B) 9.97% 
C) 10.00% 
D) 20.00%

Question 7

Which of the following statements best describes the range of possible values of the delta of a call option?

Accepted Answer

A) Lies between $- 1$
And
 $+ 1$
) 
B) Lies between $0$
And
 $+ 1$
) 
C) Lies between $- 1$
And
 $0$
) 
D) Lies between $- \infty$
And
 $+ \infty$
) 
A) Lies between $- 1$
And
 $+ 1$
) 
B) Lies between $0$
And
 $+ 1$
) 
C) Lies between $- 1$
And
 $0$
) 
D) Lies between $- \infty$
And
 $+ \infty$
)

Question 8

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.The risk-free gross return per time step is 1.001668.If a 98-strike call option is trading at $2,how much arbitrage profit can you make in present value terms?

Accepted Answer

A) $2.09 
B) $4.09 
C) $6.09 
D) $12.09 
A) $2.09 
B) $4.09 
C) $6.09 
D) $12.09

Question 9

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-free rate is 0.1668% per month in simple terms,what is the price of a 99-strike one-month put option?

Accepted Answer

A) $4.02 
B) $4.42 
C) $4.49 
D) $4.57 
A) $4.02 
B) $4.42 
C) $4.49 
D) $4.57

Question 10

In a portfolio insurance strategy,when stock prices drop,the portfolio is rebalanced by

Accepted Answer

A) Buying stock and investing at the risk-free rate. 
B) Buying stock and borrowing at the risk-free rate. 
C) Selling stock and investing at the risk-free rate. 
D) Selling stock and borrowing at the risk-free rate. 
A) Buying stock and investing at the risk-free rate. 
B) Buying stock and borrowing at the risk-free rate. 
C) Selling stock and investing at the risk-free rate. 
D) Selling stock and borrowing at the risk-free rate.

Question 11

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-free rate is 0.1668% per month in simple terms,which of the following choices best describes the replicating portfolio for one hundred 99-strike one-month call options?

Accepted Answer

A) Long 50 shares of stock and long 50 units of $1 bonds. 
B) Long 55 shares of stock and long 49 units of $1 bonds. 
C) Long 55 shares of stock and short 49 units of $1 bonds. 
D) Long 55 shares of stock and short 50 units of $1 bonds. 
A) Long 50 shares of stock and long 50 units of $1 bonds. 
B) Long 55 shares of stock and long 49 units of $1 bonds. 
C) Long 55 shares of stock and short 49 units of $1 bonds. 
D) Long 55 shares of stock and short 50 units of $1 bonds.

Question 12

Pricing options in the risk-neutral world implies that

Accepted Answer

A) Trading of options is without risk. 
B) All assets are risk-free in this world. 
C) All assets earn the risk-free rate of return. 
D) All investors are risk-neutral. 
A) Trading of options is without risk. 
B) All assets are risk-free in this world. 
C) All assets earn the risk-free rate of return. 
D) All investors are risk-neutral.

Question 13

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If an investment of a dollar at the risk-free rate returns $1.001668 after one month,and the 98-strike put option is trading at $2,how much arbitrage profit can you make in present value terms?

Accepted Answer

A) $1.93 
B) $2.92 
C) $3.93 
D) $8.00 
A) $1.93 
B) $2.92 
C) $3.93 
D) $8.00

Question 14

Suppose that in a binomial model,the stock moves up by a factor $u = e ^{ ?  \sqrt { h }}$ and down by a factor $d = e ^ { - \sigma - \sqrt { h } }$ ,where $h$ is time in years.Letting $h =$ one month and $u = 1.05$ ,what is the annualized volatility $\sigma$ of the stock?

Accepted Answer

A) 6.93% 
B) 10.39% 
C) 13.86% 
D) 16.90% 
A) 6.93% 
B) 10.39% 
C) 13.86% 
D) 16.90%

Question 15

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-neutral probability of the stock going up is equal to 0.52,what is the one-month forward price of the stock?

Accepted Answer

A) $99.48 
B) $100.40 
C) $100.48 
D) $100.52 
A) $99.48 
B) $100.40 
C) $100.48 
D) $100.52

Question 16

You hold a portfolio consisting of 300 calls (short)and 200 puts (long)on a given stock.The delta of the calls is $+ 0.62$ and the delta of the puts is $- 0.57$ .To delta hedge this portfolio,you should

Accepted Answer

A) Short 74 shares of the stock. 
B) Buy 300 shares of the stock. 
C) Buy 500 shares of the stock. 
D) Buy 74 shares of the stock. 
A) Short 74 shares of the stock. 
B) Buy 300 shares of the stock. 
C) Buy 500 shares of the stock. 
D) Buy 74 shares of the stock.

Question 17

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If an investment of a dollar at the risk-free rate returns $1.001668 after one month,what is the expected gross return of a 100-strike one-month call option under the risk-neutral probabilities?

Accepted Answer

A) 1.0010 
B) 1.0017 
C) 1.0100 
D) 1.0167 
A) 1.0010 
B) 1.0017 
C) 1.0100 
D) 1.0167

Question 18

You hold a portfolio of European options on a stock that is (i)long 200 at-the-money calls,each with a delta of $0.52$ ,(ii)short 200 at-the-money puts,and (iii)long 100 shares of stock.The aggregate delta of your portfolio is

Accepted Answer

A) 100. 
B) 108. 
C) 300. 
D) Cannot be calculated from the given information. 
A) 100. 
B) 108. 
C) 300. 
D) Cannot be calculated from the given information.

Question 19

You are long 300 at-the-money calls on Stock ABC,each with a delta of $+ 0.54$ ,and short 200 in-the-money calls on Stock XYZ,each with a delta of $+ 0.66$ .Which of the following statements is most accurate in this context?

Accepted Answer

A) The aggregate delta of your portfolio is $+ 294$
) 
B) The aggregate delta of your portfolio is $+ 30$
) 
C) The aggregate delta of your portfolio is $+ 60$
) 
D) The notion of an "aggregate portfolio delta" is not meaningful in this setting. 
A) The aggregate delta of your portfolio is $+ 294$
) 
B) The aggregate delta of your portfolio is $+ 30$
) 
C) The aggregate delta of your portfolio is $+ 60$
) 
D) The notion of an "aggregate portfolio delta" is not meaningful in this setting.

Question 20

Assuming all else is constant,which of the following statements best describes the delta of a put option?

Accepted Answer

A) The delta of a put at a stock price $S _ { 1 }$
Is greater than the delta of the same put at stock price
 $S _ { 2 } > S _ { 1 }$
) 
B) The delta of a put at a stock price $S _ { 1 }$
Is smaller than the delta of the same put at stock price
 $S _ { 2 } > S _ { 1 }$
) 
C) The delta of a put at a stock price $S _ { 1 }$
Is equal to the delta of the same put at stock price
 $S _ { 2 } > S _ { 1 }$
) 
D) None of the above is always true for all puts. 
A) The delta of a put at a stock price $S _ { 1 }$
Is greater than the delta of the same put at stock price
 $S _ { 2 } > S _ { 1 }$
) 
B) The delta of a put at a stock price $S _ { 1 }$
Is smaller than the delta of the same put at stock price
 $S _ { 2 } > S _ { 1 }$
) 
C) The delta of a put at a stock price $S _ { 1 }$
Is equal to the delta of the same put at stock price
 $S _ { 2 } > S _ { 1 }$
) 
D) None of the above is always true for all puts.

Exam 11: Option Pricing: An Introduction

The risk-neutral pricing of options

"Portfolio insurance" refers to a trading strategy in which

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-neutral probability of the stock going up is equal to 0.52,what is the price of a one-month call option at a strike price of $102?

Which of the following statements best describes the range of possible values of the delta of a call option?

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.The risk-free gross return per time step is 1.001668.If a 98-strike call option is trading at $2,how much arbitrage profit can you make in present value terms?

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-free rate is 0.1668% per month in simple terms,what is the price of a 99-strike one-month put option?

In a portfolio insurance strategy,when stock prices drop,the portfolio is rebalanced by

Pricing options in the risk-neutral world implies that

In a one-period binomial model,assume that the current stock price is $100,and that it will rise to $110 or fall to $90 after one month.If the risk-neutral probability of the stock going up is equal to 0.52,what is the one-month forward price of the stock?

You hold a portfolio consisting of 300 calls (short)and 200 puts (long)on a given stock.The delta of the calls is +0.62+ 0.62+0.62 and the delta of the puts is −0.57- 0.57−0.57 .To delta hedge this portfolio,you should

You hold a portfolio of European options on a stock that is (i)long 200 at-the-money calls,each with a delta of 0.520.520.52 ,(ii)short 200 at-the-money puts,and (iii)long 100 shares of stock.The aggregate delta of your portfolio is

You are long 300 at-the-money calls on Stock ABC,each with a delta of +0.54+ 0.54+0.54 ,and short 200 in-the-money calls on Stock XYZ,each with a delta of +0.66+ 0.66+0.66 .Which of the following statements is most accurate in this context?

Assuming all else is constant,which of the following statements best describes the delta of a put 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

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 Hjmand Libor Market Model LMM

Credit Derivative Products

Structural Models of Default Risk

Reduced-Form Models of Default Risk

Modeling Correlated Default

Filters

You hold a portfolio consisting of 300 calls (short)and 200 puts (long)on a given stock.The delta of the calls is $+ 0.62$ and the delta of the puts is $- 0.57$ .To delta hedge this portfolio,you should

You hold a portfolio of European options on a stock that is (i)long 200 at-the-money calls,each with a delta of $0.52$ ,(ii)short 200 at-the-money puts,and (iii)long 100 shares of stock.The aggregate delta of your portfolio is

You are long 300 at-the-money calls on Stock ABC,each with a delta of $+ 0.54$ ,and short 200 in-the-money calls on Stock XYZ,each with a delta of $+ 0.66$ .Which of the following statements is most accurate in this context?