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1. Problem 8.7 ; The current price of a stock is $15. In 6 months, the price will be either $18 or $13. The annual risk-free rate is 6%. Find the price of a call option on the stock that has a strike price of $14 and that expires in 6 months. (Hint: Use daily compounding.)

Answer :

P = $15

P(u) = $18

P(d) = $13

rRF = 6%

X = $14

Cu ending up option payoff = Max(18-14) = $4

Cd ending down option payoff = Max(13-14) = $0

Share of stock (Ns) = Cu – Cd / P(u) – P(d)

= $4 - $0 / $18 - $13

Share of stock = 0,8

Hedge portofolio’s payoff if stock is up = NsP(u) - Cu

= 0,8($18) - $3

= $10,4

Hedge portofolio’s payoff if stock is down = NsP(d) – Cd

= 0,8($13) - $0

= $10,4

PV of riskless payoff = $10,4 / (1+rRF/365)365(t/n)

= $7,8 / (1+0,06/365)365(0.5/1)

= $10,09

Option’s Value (VC) = NsP - Present value of riskless payoff

= 0.8 x $15 - $10,09

= $1,91

2. Problem 8.4 ; The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?

Answer :

Put option = VC – P + Xe -rRFt

Put option = $6,56 - $33 + $32-0.06x1

Put option = $3,74

Chapter 13

1. Martin Development Co. is deciding whether to proceed with Project X. The cost would be $9 million in Year 0. There is a 50% chance that X would be hugely successful and would generate annual after-tax CF of $6 million per year during years 1, 2 & 3. However, there is a 50% chance that X would be less successful and would generate only $1 million per year for the 3 years. If project X would be less successful and would generate only $1 million per year for the 3 years. If Project X is successful, it would open the door to another investment, Project Y, that would require a $10 million outlay at the end of Year 2....