3. Recall the index linked GIC that we discussed in class. The GIC has a maturity of 3 years and its payoff per a $100 investment is as follows. Suppose the S&P/TSE 60 is currently 800. For an investment of $100, you'll get: TSE 60 in 3 years (IT) Payoff Less than 800 800 (IT) 1,040 Greater than 1,040 $100 $100 + + {100[(IT 800)/800]} = $100 + 0.125(IT 800) $130 Suppose that the TSE 60 index follows a geometric Brownian motion with an expected return of 8% p.a. and a standard deviation of 20% p.a. Suppose also that the dividend yield on the index is zero (i.e., no dividend), and that the risk-free rate is 4% p.a. for all terms. (a) (3 points) Is this GIC fairly priced? (b) (2 points) What is the real-world probability that the payoff in 3 years will be greater than $100 but less than $130?