Note: in all of these problems, start with the value of your underlying asset, and build your binomial trees as we always have before: U= exp(sigma*sqrt(At)) and D=1/U. Then price the options by adjusting the risk-neutral probabilities q and 1 9 for the convenience yield: exp[(r - c) * At] - D 9 U-D 1. Assume that the S&P 500 Index level is currently 2,000 with volatility of 15% per year and dividend yield of 1.8% per year. The current risk-free rate of return is 1.2% per year. In a 12-step binomial tree (with one step per month), calculate the value and optimal exercise boundary for a one-year American call option on the S&P 500 index with strike price of 2,000. (Note that options on the index pay $1 per index point, so if the index ends up at 2,123, the payoff on a 2,000 call would be (2,123 2,000) x $1 = $123). Build your tree of underlying values using whole numbers, and then present your option value tree with two decimals. Make sure you highlight the cells where exercise takes place. Note: in all of these problems, start with the value of your underlying asset, and build your binomial trees as we always have before: U= exp(sigma*sqrt(At)) and D=1/U. Then price the options by adjusting the risk-neutral probabilities q and 1 9 for the convenience yield: exp[(r - c) * At] - D 9 U-D 1. Assume that the S&P 500 Index level is currently 2,000 with volatility of 15% per year and dividend yield of 1.8% per year. The current risk-free rate of return is 1.2% per year. In a 12-step binomial tree (with one step per month), calculate the value and optimal exercise boundary for a one-year American call option on the S&P 500 index with strike price of 2,000. (Note that options on the index pay $1 per index point, so if the index ends up at 2,123, the payoff on a 2,000 call would be (2,123 2,000) x $1 = $123). Build your tree of underlying values using whole numbers, and then present your option value tree with two decimals. Make sure you highlight the cells where exercise takes place