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Exam 20: Brownian Motion and Itos Lemma

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Question 1

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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.

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

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Question 2

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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

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Question 3

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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:

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

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

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

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

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) = $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 -0.65,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 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 $\sqrt[5]{Q}$ ?

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.

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

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

Provide a definition of Brownian motion.

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

Define the term drift.

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?