Let us consider a stock (called "stock A") whose price today is €12. Suppose that in six months' time the price can only go up to €16 or down to €10. Suppose the interest rate is 10% per annum continuously compounded. Let us consider a call option (called "call option B") written on this stock, with maturity date of 6 months and strike price €13. (a) Determine the fair price c for this call option (show all the steps of your work). Assume that the seller of call options B starts with zero capital, sells 100 call options (each at the fair price c obtained in the previous question), and borrows money to buy A shares of the stock A. (b) How many shares should he buy in order to run no risk at the end of the six months period?
Let us consider a stock (called "stock A") whose price today is €12. Suppose
that in six months' time the price can only go up to €16 or down to €10.
Suppose the interest rate is 10% per annum continuously compounded.
Let us consider a call option (called "call option B") written on this stock,
with maturity date of 6 months and strike price €13.
(a) Determine the fair price c for this call option (show all the steps of your
work).
Assume that the seller of call options B starts with zero capital, sells 100
call options (each at the fair price c obtained in the previous question), and
borrows money to buy A shares of the stock A.
(b) How many shares should he buy in order to run no risk at the end of the
six months period?
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