CF chapter 21

Question 1

Binomial model (option pricing)

Answer 1

Stock price follows a ‘binomial tree’ with a given number of periods

In every period the stock price may either go up or down by a known amount or percentage

The one-period risk-free interest rate is given

Question 2

Delta

Answer 2

Number of shares purchasedB

Question 3

B

Answer 3

Initial investment in bonds

Question 4

Binomial pricing formula stock goes up

Answer 4

Su +(1+rf)*B = Cu

Cu = call price up
Su = stock price up

Question 5

Binomial pricing formula stock goes down

Answer 5

Sd + (1+rf)*B = Cd

Sd = stock price down
Cu = call price down

Question 6

Delta formula

Answer 6

Cu - Cd /Su - Sd

or

-[N(-d1)]

Question 7

B formula

Answer 7

Cd - SD * delta / 1+ rf

or

PV(K)∙[N(-d2)]

Question 8

Option price in the binomial model

Answer 8

C = S *D + B

Question 9

Black sholes model formula

Answer 9

C = S*N(d1) −PV(K)∙N(d2)

Question 10

d(1) formula

Answer 10

ln(S/PV(K))/(omegasqr(T) + omegasqr(T)/2

Question 11

d(2) formula

Answer 11

1-omega*sqr(T)

Question 12

Black-Scholes Price of a European Put Option on a Non-Dividend-Paying Stock

Answer 12

P = PV(K )[1 - N(d2 )] - S[1 - N(d1)]

Question 13

P (risk free probabilitiess p and 1-p)

Answer 13

P = (1+rf)*S -Sd/Su - Sd