A stock price is currently $10. It is known that at the end of three months it will be either $11 or $8.5. The riskfree interest rate is 5% per annum with continuous compounding. Suppose S_T is the stock

price at the end of three months.

(a) What is the value of a derivative that pays off ln(S_T) at this time? Use both the no arbitrage

and risk neutral valuation approach.

(b) What is the delta of the derivative in part (a)? How do you interpret that number?