Deck 22: Risk-Neutral and Martingale Pricing

Question 1

How do asset values differ between using a traditional DCF approach and a stochastic discount factor approach?

Answer 1

When implemented correctly,the two approaches will give the same present value.The DCF uses asset-specific state-dependent discount rates and the stochastic approach uses asset-independent,state-dependent discount rates.

Question 2

The case where the zero coupon bond is selected as the numeraire under a risky asset method results in a measure called the:

A) Drift measure
B) Forward measure
C) Money market measure
D) Spread measure

Answer 2

B

Question 3

The ratio of the future uncertain martingale utility to the present known martingale utility is called:

A) Brownian motion
B) Change of measure
C) Stochastic discount factor
D) Utility function

Answer 3

C

Question 4

For a utility function that exhibits decreasing martingale utility,the martingale utility is low when:

A) Consumption and utility are low
B) Consumption and utility are high
C) Consumption is low and utility is high
D) Consumption is high and utility is low

Question 5

The pricing of derivatives is linked to the decisions investors make relative to:

A) Black-Scholes variables
B) Money markets
C) Portfolios
D) T-bills

Question 6

What does Girsanov's theorem tell us about drift and Brownian motion?

Question 7

In the first-order condition for portfolio selection,explain the meaning of equilibrium.

Question 8

The process of moving from one probability distribution to another is called:

A) Brownian motion
B) Change of measure
C) Stochastic discount factor
D) Utility function

Question 9

In martingale pricing,the observed price of a stock follows a process which substitutes what variable for alpha?

A) Delta
B) Epsilon
C) Money market rate
D) Risk-free rate

Question 10

What aspect of risk-neutral pricing valuation links it to portfolio selection?

Question 11

It can be said that Girsanov's theorem shows the equivalence of which two items?

A) Change of drift and change of measure
B) Change of numeraire and change of measure
C) Change of drift and change of numeraire
D) Change of numeraire and change of process

Question 12

When defining a change in measure,a redefining of the units in which a payoff is measured is called:

A) Brownian motion
B) Change of numeraire
C) Stochastic discount factor
D) Utility function

Question 13

Randomly divide the class into two groups.Give one group the task of defending Warren Buffet's position on valuing put options.Have the other group disagree with Buffet's position.Moderate a discussion of the two,listing the pros and cons on the board.

Question 14

The risk-neutral measure arises when we select ________ as the numeraire.

A) Asset portfolio
B) Corporate bond
C) Treasury bond
D) Money market account

Question 15

In the case of a European Outperformance Option,we assume the strike asset is:

A) Cash
B) A money market fund
C) A stock or an index
D) A zero-coupon bond

Question 16

How do probabilities change with a change of measure?

Question 17

For a utility function that exhibits decreasing martingale utility,the martingale utility is high when:

A) Consumption and utility are low
B) Consumption and utility are high
C) Consumption is low and utility is high
D) Consumption is high and utility is low

Question 18

Which of the following is not commonly used as a numeraire?

A) Futures contract
B) Money market account
C) Risky asset
D) Zero coupon bond

Question 19

The primary link between Brownian motion and Girsanov's theorem relates to which variable?

A) Drift
B) Numeraire
C) Returns
D) Standard deviation