Problem 1
ABC stock has a share price of $150 today. All rates of interest are 3% per annum on a continuously compounded basis. A one-year European call option on one share of stock struck at $147 is worth $15. Finally, ABC is scheduled to pay the following dividends per share over the next year: a dividend of $3.0 per share in three months and a dividend of $3.0 per share in nine months.
a) Derive the forward price of the stock for delivery in one year.
b) What is the value of an otherwise identical European put option?
Problem 2
All index options are European and have a one year maturity. The annual continuously compounded financing rate is 5%, the spot price of the underlying index is $100, and the continuously compounded annual dividend yield on the index is 2%. Finally, you know that a call option with a strike of $100 is worth $12.00 and a call option with a strike of $120 is worth $5.00.
a) Derive the value of a put with a strike of $100.
b) Derive the value of a put with a strike of $120.
c) Derive an upper bound on the value of a put option with a strike of $110.