Deck 20: Brownian Motion and Itos Lemma

Question 1

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/ ?

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

Answer 1

D

Question 2

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

Answer 2

The distribution dictated is lognormal and we are able to describe the path taken by stock prices.

Question 3

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 ?

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

Answer 3

C

Question 4

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

Question 5

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?

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

Question 6

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.

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

Question 7

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/ ?

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

Question 8

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.

Question 9

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 ? Use formula 20.29.

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

Question 10

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.

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

Question 11

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

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 12

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

Question 13

Provide a definition of Brownian motion.

Question 14

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

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

Question 15

Define the term drift.

Question 16

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:

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

Question 17

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

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

Question 18

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

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

Question 19

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 ? Use formula 20.29.

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