Homework Problem 18_1

An analysis of HL Corporation suggests that in the next year the price of its stock will be either $50 or $30.The current price is $40.The 1-year riskless rate is 10%.

Consider a call option that expires in one year with an exercise price of $35.

a) The Replicating Portfolio is a portfolio of stocks and bonds that exactly replicates the payoff of the call option under all conditions, in this case the two states.

What portfolio of stocks (number of shares bought or shorted) and bonds (dollars borrowed/shorted or lent/long) that has same payoff if this Call option?

b) What is the fair value of this call? and why?

c) Create riskless hedge with the call and stock. A riskless hedge is a portfolio of stocks and calls that have the same payoff in all conditions, in this case the two states.

For example, Write 1 calls and buy .75 shares or Buy 1 call and short .75 shares.

d) An arbitrage is a strategy that has all positive cash flows with no investment or negative cash flows.

How would you create arbitrage if the Call were priced at $15?

e) How would you create arbitrage if the Option were priced at $5?