6. Option-like Instruments (15 points) A customized Guaranteed Investment Certificate (GIC) offered by a bank guarantees that investors will receive a net return in percentage during a 6-month period that is the greater of (1) zero and (2) 40% of the 6-month simple net return provided by a market index. An investor is planning to put an amount of $L in the instrument. (a) (5 points) Mathematically describe the dollar net return of the instrument with the payoff of an option on the index, assuming $L is invested and using the same notations in the lecture. [The result should be a function of L and the payoff max{0, ST X} (with X = S0) of an option. 3 (b) (10 points) What is todays value of that dollar net return in (a), according to the Black-Scholes model, assuming the following parameters: the risk-free rate is 4% per annum, the continuous dividend yield on the index is 2% per annum, and the volatility of the continuously compounding returns of the index is 25% per annum, and L = $100, 000