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 ST is the stock price at the end of three months.

(a) What is the value of a derivative that pays off ln(ST) 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?