The following questions are based on option pricing on the one-time step binomial tree world. Suppose a stock S = $100 at time 0. At time 1, the stock can be either to $150 or down to $75. Risk-free rate is 0. (2 points each)

Question 1

What is the delta of at-the-money call option (That is, call with strike price $100)?

a) 1/3

b) 2/3

C) 1

d) 4/3

Question 2

What is the price of at-the-money call option (That is, call with strike price $100)?

a) $50/3

b) $100/3

c) $50

d) $200/3

Question 3

What is the delta of at-the-money put option (That is, put with strike price 100)?

a) -1/3

b) -2/3

c) -1

d) -4/3

Question 4

What is the price of at-the-money put option (That is, put with strike price $100)?

a) $50/3

b) $100/3

c) $50

d) $200/3

Question 5

What is the delta of an exotic option that pays $100 if the underlying stock price at time 1 is above $100, and pays nothing otherwise?

a) 1/3

b) 2/3

c) 1

d) 4/3

Question 6

What is the price of an exotic option that pays $100 if the underlying stock price at time 1 is above $100, and pays nothing otherwise?

a) $50/3

b) $100/3

c) $50

d) $200/3

Question 7

What is the delta of an exotic option that pays $100 if the underlying stock price at time 1 is below $100, and pays nothing otherwise?

a) -1/3

b) -2/3

c) -1

d) -4/3

Question 8

What is the price of an exotic option that pays $100 if the underlying stock price at time 1 is below $100, and pays nothing otherwise?

a) $50/3

b) $100/3

c) $50

d) $200/3

Question 9

What is the price of a unit security whose pay off at time step 1 is 1 when the stock is up, and 0 when the stock is down?

a) $1/3

b) $2/3

c) $1

d) $4/3

Question 10

What is the price of a unit security whose pay off at time step 1 is 1 when the stock is down, and 0 when the stock is up?

a) $1/3

b) $2/3

c) $1

d) $4/3