Question 1

The value of Z(t)at any point in time can be described as a process in which there is a cumulative effect of infinitely small movements.This process is called:

Accepted Answer

A)  Ornstein-Uhlenbeck 
B)  Diffusion 
C)  Ito 
D)  Geometric 
A)  Ornstein-Uhlenbeck 
B)  Diffusion 
C)  Ito 
D)  Geometric B

Question 2

For purposes of option pricing,when the movement of a stock price follows a geometric Brownian motion,the stock price is said to follow which type of distribution?

Accepted Answer

A)  Bimodal 
B)  Latin hypercube 
C)  Lognormal 
D)  Normal 
A)  Bimodal 
B)  Latin hypercube 
C)  Lognormal 
D)  Normal C

Question 3

Assume the following: LN(S)and LN(Q)have a correlation coefficient of -0.65,S(0)= 55,Q(0)= 60,r = 0.04,σs = 0.22 σQ = 0.15,and dividends = 0.Using formula 20.39,what is the price of a claim that pays Q/ $\sqrt{S}$ ?

Accepted Answer

A)  $8.16 
B)  $9.16 
C)  $10.16 
D)  $11.16 
A)  $8.16 
B)  $9.16 
C)  $10.16 
D)  $11.16 A

Question 4

Assume a stock price of S(0)= $62.00,r = 0.05,σ = 0.30,and dividend = 0.What is the price of a claim that pays $ \sqrt{S} $ ? Use formula 20.29.

Accepted Answer

A)  $7.59 
B)  $8.59 
C)  $9.59 
D)  $10.59 
A)  $7.59 
B)  $8.59 
C)  $9.59 
D)  $10.59

Question 5

Why is Brownian motion the foundation for modern derivatives pricing models? Attempt to elicit responses that understand the shortcomings of using this motion for just asset pricing and the advantages in risk measurement.

Accepted Answer

Brownian motion is the foundation for mo

Question 6

A Brownian motion is a stochastic process that can be described as a:

Accepted Answer

A)  Pattern of movements with continuous movements 
B)  Pattern of movements with discrete movements 
C)  Random walk with continuous movements 
D)  Random walk with discrete movements 
A)  Pattern of movements with continuous movements 
B)  Pattern of movements with discrete movements 
C)  Random walk with continuous movements 
D)  Random walk with discrete movements

Question 7

When considering drift and noise,how would you explain price movements over smaller and smaller time intervals?

Accepted Answer

As time decreases dr

Question 8

The deterministic drift of a pure Brownian motion that is virtually undetectable is sometimes referred to as the:

Accepted Answer

A)  Distribution 
B)  Expected return 
C)  Random walk 
D)  Standard deviation 
A)  Distribution 
B)  Expected return 
C)  Random walk 
D)  Standard deviation

Question 9

What are two important implications of assuming that prices follow a geometric Brownian motion?

Accepted Answer

The distribution dic

Question 10

Assume the following: LN(S)and LN(Q)have a correlation coefficient of -0.20,S(0)= 45,S(Q)= 55,r = 0.03,σs = 0.18 σQ = 0.28,and no dividends.Using formula 20.39,what is the price of a claim that pays 1/ $\sqrt{Q S}$
 ?

Accepted Answer

A)  $3.02 
B)  $2.02 
C)  $1.02 
D)  $0.02 
A)  $3.02 
B)  $2.02 
C)  $1.02 
D)  $0.02

Question 11

Assume a stock price of S(0)= $80.00,r = 0.05,σ = 0.35,and dividend = 0.01.What is the price of a claim that pays S⁻²/³? Use formula 20.29.

Accepted Answer

A)  $0.25 
B)  $0.35 
C)  $0.05 
D)  $0.15 
A)  $0.25 
B)  $0.35 
C)  $0.05 
D)  $0.15

Question 12

Assume a stock price of S(0)= $83.00,r = 0.045,σ = 0.25,and dividend = 0.02.What is the price of a claim that pays S³? Use formula 20.29.

Accepted Answer

A)  $423,323 
B)  $710,695 
C)  $624,165 
D)  $818,123 
A)  $423,323 
B)  $710,695 
C)  $624,165 
D)  $818,123

Question 13

Assume a stock price of S(0)= $45.00,r = 0.03,σ = 0.40,and dividend = 0.015.What is the price of a claim that pays $ \sqrt[3]{S} $ ? Use formula 20.29.

Accepted Answer

A)  $6.41 
B)  $5.41 
C)  $4.41 
D)  $3.41 
A)  $6.41 
B)  $5.41 
C)  $4.41 
D)  $3.41

Question 14

Define the term drift.

Accepted Answer

The expected change

Question 15

A modification to the Brownian process that permits mean reversion is called:

Accepted Answer

A)  Ornstein-Uhlenbeck 
B)  Diffusion 
C)  Ito 
D)  Geometric 
A)  Ornstein-Uhlenbeck 
B)  Diffusion 
C)  Ito 
D)  Geometric

Question 16

Assume the following: LN(S)and LN(Q)have a correlation coefficient of 0.40,S(0)= 60,Q(0)= 60,r = 0.05,σs = 0.30 σQ = 0.25,and dividend = 0.Using formula 20.39,what is the price of a claim that pays $ \sqrt[5]{Q} $ ?

Accepted Answer

A)  $243.96 
B)  $322.96 
C)  $479.96 
D)  $532.96 
A)  $243.96 
B)  $322.96 
C)  $479.96 
D)  $532.96

Question 17

What is the relationship of the Sharpe ratios and risk premiums between stocks and options?

Accepted Answer

Since volatility of options is

Question 18

Provide a definition of Brownian motion.

Accepted Answer

A random walk occurr

Question 19

A modification to the Brownian process in which the drift and volatility depend on the stock price is called:

Accepted Answer

A)  Ornstein-Uhlenbeck 
B)  Diffusion 
C)  Ito 
D)  Geometric 
A)  Ornstein-Uhlenbeck 
B)  Diffusion 
C)  Ito 
D)  Geometric

Exam 20: Brownian Motion and Itos Lemma

The value of Z(t)at any point in time can be described as a process in which there is a cumulative effect of infinitely small movements.This process is called:

For purposes of option pricing,when the movement of a stock price follows a geometric Brownian motion,the stock price is said to follow which type of distribution?

Assume the following: LN(S)and LN(Q)have a correlation coefficient of -0.65,S(0)= 55,Q(0)= 60,r = 0.04,σs = 0.22 σQ = 0.15,and dividends = 0.Using formula 20.39,what is the price of a claim that pays Q/ S\sqrt{S}S​ ?

Assume a stock price of S(0)= $62.00,r = 0.05,σ = 0.30,and dividend = 0.What is the price of a claim that pays S \sqrt{S} S​ ? Use formula 20.29.

Why is Brownian motion the foundation for modern derivatives pricing models? Attempt to elicit responses that understand the shortcomings of using this motion for just asset pricing and the advantages in risk measurement.

A Brownian motion is a stochastic process that can be described as a:

When considering drift and noise,how would you explain price movements over smaller and smaller time intervals?

The deterministic drift of a pure Brownian motion that is virtually undetectable is sometimes referred to as the:

What are two important implications of assuming that prices follow a geometric Brownian motion?

Assume the following: LN(S)and LN(Q)have a correlation coefficient of -0.20,S(0)= 45,S(Q)= 55,r = 0.03,σs = 0.18 σQ = 0.28,and no dividends.Using formula 20.39,what is the price of a claim that pays 1/ QS\sqrt{Q S}QS​ ?

Assume a stock price of S(0)= $80.00,r = 0.05,σ = 0.35,and dividend = 0.01.What is the price of a claim that pays S⁻²/³? Use formula 20.29.

Assume a stock price of S(0)= $83.00,r = 0.045,σ = 0.25,and dividend = 0.02.What is the price of a claim that pays S³? Use formula 20.29.

Assume a stock price of S(0)= $45.00,r = 0.03,σ = 0.40,and dividend = 0.015.What is the price of a claim that pays S3 \sqrt[3]{S} 3S​ ? Use formula 20.29.

Define the term drift.

A modification to the Brownian process that permits mean reversion is called:

Assume the following: LN(S)and LN(Q)have a correlation coefficient of 0.40,S(0)= 60,Q(0)= 60,r = 0.05,σs = 0.30 σQ = 0.25,and dividend = 0.Using formula 20.39,what is the price of a claim that pays Q5 \sqrt[5]{Q} 5Q​ ?

What is the relationship of the Sharpe ratios and risk premiums between stocks and options?

Provide a definition of Brownian motion.

A modification to the Brownian process in which the drift and volatility depend on the stock price is called:

Introduction to Derivatives

An Introduction to Forwards and Options

Insurance, collars, and Other Strategies

Introduction to Risk Management

Financial Forwards and Futures

Commodity Forwards and Futures

Interest Rate Forwards and Futures

Swaps

Parity and Other Option Relationships

Binomial Option Pricing: Basic Concepts

Binomial Option Pricing: Selected Topics

The Black-Scholes Formula

Market-Making and Delta-Hedging

Exotic Options: I

Financial Engineering and Security Design

Corporate Applications

Real Options

The Lognormal Distribution

Monte Carlo Valuation

The Black-Scholes-Merton Equation

Risk-Neutral and Martingale Pricing

Exotic Options: 2

Volatility

Interest Rate and Bond Derivatives

Value at Risk

Credit Risk

Filters

Assume the following: LN(S)and LN(Q)have a correlation coefficient of -0.65,S(0)= 55,Q(0)= 60,r = 0.04,σs = 0.22 σQ = 0.15,and dividends = 0.Using formula 20.39,what is the price of a claim that pays Q/ $\sqrt{S}$ ?

Assume a stock price of S(0)= $62.00,r = 0.05,σ = 0.30,and dividend = 0.What is the price of a claim that pays $\sqrt{S}$ ? Use formula 20.29.

Assume the following: LN(S)and LN(Q)have a correlation coefficient of -0.20,S(0)= 45,S(Q)= 55,r = 0.03,σs = 0.18 σQ = 0.28,and no dividends.Using formula 20.39,what is the price of a claim that pays 1/ $\sqrt{Q S}$ ?

Assume a stock price of S(0)= $45.00,r = 0.03,σ = 0.40,and dividend = 0.015.What is the price of a claim that pays $\sqrt[3]{S}$ ? Use formula 20.29.

Assume the following: LN(S)and LN(Q)have a correlation coefficient of 0.40,S(0)= 60,Q(0)= 60,r = 0.05,σs = 0.30 σQ = 0.25,and dividend = 0.Using formula 20.39,what is the price of a claim that pays $\sqrt[5]{Q}$ ?