Exam: CH 13 Black Scholes model

Question 1

What does this Term µ∆t stand for?

Answer 1

• the expected value of the return for time delta t

Question 2

What is the geometric mean?

Answer 2

• considers the successive returns are not independent
  and how the returns would actually be earned over the five years period.
  Also, returns are assumed to be continuously compounded

Question 3

How does a variable have a lognormal distribution?

Answer 3

• A variable has a lognormal distribution if the natural log of the variable is normally distributed

Question 4

What is volatility?

Answer 4

• The volatility is the standard deviation of the
  continuously compounded rate of return in 1
  year

Question 5

How is time measured and why?

Answer 5

• Time is usually measured in trading days not calendar days because volatility is usually greater when the assets are trading.

Question 6

What is the implied volatility of an option?

Answer 6

• is the volatility for which the Black-Scholes price equals the market price

Question 7

What is historical volatility?

Answer 7

• A volatility estimated from historical data

Question 8

What is the difference between implied and hitorical volatility?

Answer 8

• Implied is forward looking
  Whereas
• Historical volatility is backward looking

Question 9

Can the Black-Scholes model be used to price american call/put option?

Answer 9

• No they cannot
• An American call on non-dividend-paying stock should
  never be exercised
• An American call on non-dividend-paying stock should
  should only ever be exercised immediately prior to an
  ex-dividend date