Deck 12: The Black-Scholes Formula

Question 1

What is the price of a $30 strike put? Assume S = $28.50,σ = 0.32,r = 0.04,the stock pays a 1.0% continuous dividend and the option expires in 110 days?

A) $2.70
B) $2.10
C) $1.80
D) $1.20

Answer 1

A

Question 2

Assume that an investor is currently holding a reverse straddle position (i.e.a short put and short call),which is currently a profitable investment.All else being equal,what would this investor like to happen to vega?

A) Decrease
B) Increase
C) Stay constant
D) Indifferent

Answer 2

A

Question 3

Suppose the spot exchange rate is $1.43 per British pound and the strike on a dollar denominated pound call is $1.30.Assume r = 0.045,rf = 0.06,σ = 0.15 and the option expires in 180 days.What is the call option price?

A) $0.133
B) $0.143
C) $0.153
D) $0.163

Answer 3

A

Question 4

Assume that a $50 strike call has a 3.0% continuous dividend,σ = 0.27,r = 0.06 and 60 days from expiration.What is the gamma for a stock price movement from $48.00 to $49.00?

A) 0.046
B) 0.074
C) 0.089
D) 0.099

Question 5

What is the price of a $25 strike call? Assume S = $23.50,σ = 0.24,r = 0.055,the stock pays a 2.5% continuous dividend and the option expires in 45 days?

A) $0.60
B) $0.50
C) $0.40
D) $0.30

Question 6

What is the delta on a $25 strike put? Assume S = $24.00,σ = 0.35,r = 0.06,the stock pays a 2.0% continuous dividend and the option expires in 40 days?

A) 0.582
B) 0.602
C) 0.662
D) 0.702

Question 7

As the date of expiration approaches,what change in theta might counteract or slow down the drop in the option price?

A) Decrease
B) Increase
C) Stay constant
D) Indifferent

Question 8

Draw a payoff diagram for a long put position,depicting options that expire at 0,30 and 60 days.

Question 9

What is the price of a $60 strike put? Assume S = $63.75,σ = 0.20,r = 0.055,the stock pays no dividend and the option expires in 50 days?

A) $0.66
B) $0.55
C) $0.44
D) $0.33

Question 10

Suppose the 120-day futures price on crude oil is $115.00 per barrel and the volatility is 20.0%.Assume interest rates are 3.5%.What is the price of a $110 strike call futures option that expires in 120 days?

A) $3.09
B) $2.99
C) $2.89
D) $2.79

Question 11

If an investor is speculating with a long call position,what is the most likely preference of the investor,relative to a change in rho?

A) Decrease
B) Increase
C) Stay constant
D) Indifferent

Question 12

Which Greek is also called time decay and why?

Question 13

Assume that a $60 strike call has a 2.0% continuous dividend,r = 0.05,and the stock price is $61.00.What is the theta of the option as the expiration time declines from 60 to 50 days?

A) -0.52
B) -0.42
C) -0.32
D) -0.22

Question 14

Suppose the 180-day futures price on crude oil is $110.00 per barrel and the volatility is 20.0%.Assume interest rates are 3.5%.What is the price of a $120 strike call futures option that expires in 180 days?

A) $1.89
B) $2.19
C) $2.59
D) $3.09

Question 15

Assume that a $55 strike call has a 1.5% continuous dividend,r = 0.05 and the stock price is $50.00.If the option has 45 days until expiration,what is the vega,given a shift in volatility from 33.0% to 34.0%?

A) 0.20
B) 0.15
C) 0.10
D) 0.05

Question 16

Suppose the spot exchange rate is $1.22 per British pound and the strike on a dollar denominated pound put is $1.20.Assume r = 0.04,rf = 0.05,σ = 0.20 and the option expires in 270 days.What is the put option price?

A) $0.075
B) $0.085
C) $0.095
D) $0.105

Question 17

Assume that a $75 strike call has a 1.0% continuous dividend,90 days until expiration and stock price of $72.00.What is the rho of the option as the interest rate changes from 6.0% to 5.0%?

A) 0.07
B) 0.12
C) 0.16
D) 0.20

Question 18

What is the delta on a $20 strike call? Assume S = $22.00,σ = 0.30,r = 0.05,the stock pays a 1.0% continuous dividend and the option expires in 80 days?

A) 0.790
B) 0.820
C) 0.850
D) 0.880

Question 19

Suppose a $60 strike call has 45 days until expiration and pays a 1.5% continuous dividend.Assume S = $58.50,σ = 0.25,and r = 0.06.What is the option elasticity given an immediate price increase of $1.50?

A) 24.61
B) 18.61
C) 14.61
D) 9.61

Question 20

What is the price of a $35 strike call? Assume S = $38.50,σ = 0.25,r = 0.06,the stock pays no dividend and the option expires in 45 days.

A) $3.50
B) $3.65
C) $3.80
D) $3.95

Question 21

What is the difference between a standard bull spread and a calendar bull spread?

Question 22

Why do we care about Greeks? Use this as an opportunity to introduce students to option strategies.Ask students to create simple strategies such as covered calls.Introduce Greeks and show how "not all covered calls are created equal." Encourage the class to explain how the Greeks tell us which options are better to use than others.

Question 23

What unique feature about perpetual options makes it possible to derive a valuation formula?

Question 24

What is the difference between implied volatility and historical volatility?