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.

Question 2

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 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.

Question 4

In the binomial model, if the stock moves up by a factor $u$ and down by a factor $d$ , and a $1 investment in a risk-free bond returns an amount $R$ per time step, which of the following statements is true in a market that is free from arbitrage?

Accepted Answer

A)  $d < u < R$ 
B)  $\mathcal { U } < R < d$ 
C)  $d < R < u$ 
D)  $R < d < u$ 
A)  $d < u < R$ 
B)  $\mathcal { U } < R < d$ 
C)  $d < R < u$ 
D)  $R < d < u$

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 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 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 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

The risk-neutral pricing of options

"Portfolio insurance" refers to a trading strategy in which

In the binomial model, if the stock moves up by a factor $u$ and down by a factor $d$ , and a $1 investment in a risk-free bond returns an amount $R$ per time step, which of the following statements is true in a market that is free from arbitrage?

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?

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 HJM and Libor Market Model LMM

Credit Derivative Products

Structural Models of Default Risk

Reduced-Form Models of Default Risk

Modeling Correlated Default

Filters

Exam 11: Option Pricing: an Introduction

The risk-neutral pricing of options

"Portfolio insurance" refers to a trading strategy in which

In the binomial model, if the stock moves up by a factor uuu and down by a factor ddd , and a $1 investment in a risk-free bond returns an amount RRR per time step, which of the following statements is true in a market that is free from arbitrage?

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?

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 HJM and Libor Market Model LMM

Credit Derivative Products

Structural Models of Default Risk

Reduced-Form Models of Default Risk

Modeling Correlated Default

Filters

In the binomial model, if the stock moves up by a factor $u$ and down by a factor $d$ , and a $1 investment in a risk-free bond returns an amount $R$ per time step, which of the following statements is true in a market that is free from arbitrage?